CN102150378B - Codebook design method for multiple input multiple output system and method for using codebook - Google Patents

Abstract

A multiple input multiple output (MIMO) communication method using a codebook is provided. The MIMO communication method may use one or more codebooks and the codebooks may change according to a transmission rank, a channel state of a user terminal, and/ or a number of feedback bits. The one or more codebooks may be adaptively updated according to a time correlation coefficient of a channel.

Description

For the code book method for designing of multi-input multi-output system and the method for use code book

Technical field

The following description relates to a kind of code book using in multiple-input and multiple-output (MIMO) communication system.

Background technology

For example carrying out multiple research, so that high-quality in various types of multimedia services (, voice service) support of wireless communication environment and high-speed transfer of data to be provided.Develop rapidly with the technology of using multi channel multiple-input and multiple-output (MIMO) communication system to be associated.

In MIMO communication system, base station and terminal can be used code book to suitably coordinate with channel circumstance.Particular space can be quantified as a plurality of code words.By quantizing a plurality of code words of particular space generation, can be stored in base station and terminal.According to the dimension of channel matrix, each code word can be vector or matrix.

For example, the channel that each terminal can be based on forming between base station and each terminal is selected and the corresponding matrix of channel information or vector from be included in matrix code book or vector.Base station also can receive matrix or the vector based on codebook selecting, thus identification channel information.In the time of can carrying out in base station beam forming or send signal transmission by many antennas, use matrix or the vector of selecting.

Therefore, need the code book of good design to improve the performance of MIMO communication system.

Summary of the invention

A general aspect, multiple-input and multiple-output (MIMO) communication system method comprises: storage comprises the code book of at least one matrix or vector; Determine the corresponding transmission rank of quantity with data flow; According to the channel status of at least one user terminal and transmission rank; At least one matrix or vector that use is included in code book produce pre-coding matrix, use pre-coding matrix to carry out precoding to data stream.

In another general aspect, a kind of MIMO communication means comprises: storage comprises the code book of at least one matrix or vector; The time correlation coefficient (ρ) that use is formed at the channel between at least one user terminal and base station upgrades code book; At least one matrix or vector that use is included in the code book of renewal produce pre-coding matrix; Use pre-coding matrix to carry out precoding to data stream.

The step of upgrading precoding can comprise: previous pre-coding matrix is updated to new pre-coding matrix.

The step of upgrading code book can comprise: use following equation to upgrade code book:

${\widetilde{\mathrm{\Θ}}}_i=\underset{{\widetilde{\mathrm{\Θ}}}_i}{\arg \min }{\left|\right|{\mathrm{\Ψ}}_i(\mathrm{\ρ},{\mathrm{\Θ}}_i)-{\widetilde{\mathrm{\Θ}}}_i\left|\right|}_F.$

Here,

i=1,2,3 ..., 2 ^b, B represents the quantity of feedback bits, Θ _iexpression is as code book

unitary matrice or the diagonal matrix of i element, I representation unit matrix, || x|| _fthe Frobenious norm that represents x.

represent the code book upgrading

i element.

To Ψ _i(ρ, Θ _i) execution singular value decomposition (SVD), Ψ _i(ρ, Θ _i) can be represented as

represent B _iconjugate matrices.Above-mentioned equation

can be optimised for:

can use upgrade code book.

The step of upgrading code book comprises: with following equation, upgrade code book:

${\widetilde{\mathrm{\Θ}}}_i={\left[{\mathrm{\Ψ}}_i{(\mathrm{\ρ},{\mathrm{\Θ}}_i)}^{*}{\mathrm{\Ψ}}_i(\mathrm{\ρ},{\mathrm{\Θ}}_i)\right]}^{-1/2}{\mathrm{\Ψ}}_i(\mathrm{\ρ},{\mathrm{\Θ}}_i)$

Here,

represent the code book upgrading

i element, i=1,2,3 ..., 2 ^b, Θ _iexpression is as code book

unitary matrice or the diagonal matrix of i element, I representation unit matrix.

In another general aspect, a kind of base station for alone family multiple-input and multiple-output (MIMO) communication system comprises: memory, storage comprises a plurality of code word matrix C of 4 * 1 _1,1, C _2,1, C _3,1, C _4,1, C _5,1, C _6,1, C _7,1, C _8,1, C _9,1, C _10,1, C _11,1, C _12,1, C _13,1, C _14,1, C _15,1and C _16,1code book; Precoder, is used described code book to the data flow being sent out is carried out to precoding, wherein, and by a plurality of code word matrix described in lower table definition:

Precoder can at least one code word matrix based in described a plurality of code word matrix calculate pre-coding matrix, and uses pre-coding matrix to carry out precoding to data stream.

Described base station also can comprise: message recipient, from terminal receiving feedback information, wherein, precoder is used feedback information and code book to carry out precoding to data stream.

Precoder can be based on calculating pre-coding matrix with the corresponding code word matrix of feedback information in described a plurality of code word matrix, and use pre-coding matrix to carry out precoding to data stream.

Feedback information can comprise the index information of terminal preferred code word matrix from described a plurality of code word matrix.

Described base station also can comprise four transmitting antennas, and wherein, described code book is for transmission rank 1.

In another general aspect, a kind of base station of multi-user MIMO communication system comprises: memory, storage comprises a plurality of code word matrix C of 4 * 1 _1,1, C _2,1, C _3,1, C _4,1, C _5,1, C _6,1, C _7,1, C _8,1, C _9,1, C _10,1, C _11,1, C _12,1, C _13,1, C _14,1, C _15,1and C _16,1code book; Precoder, is used described code book to the data flow being sent out is carried out to precoding, wherein, and by a plurality of code word matrix described in lower table definition:

Described base station also can comprise: message recipient, from least two terminal receiving feedback informations, wherein, at least one feedback information that precoder use receives from described at least two terminals and described code book carry out precoding at least one data flow.

In another general aspect, a kind of terminal of MIMO communication system comprises: memory, storage comprises a plurality of code word matrix C of 4 * 1 _1,1, C _2,1, C _3,1, C _4,1, C _5,1, C _6,1, C _7,1, C _8,1, C _9,1, C _10,1, C _11,1, C _12,1, C _13,1, C _14,1, C _15,1and C _16,1code book; Feedback unit, the feedback information that the preferred code word matrix with described a plurality of code word matrix is associated feeds back to base station, wherein, by a plurality of code word matrix described in lower table definition:

Described terminal also can comprise: channel estimating unit, estimate the channel between base station and terminal, and wherein, feedback unit feeds back to base station by the definite feedback information of channel based on estimating.

In another general aspect, a kind of storage medium of having stored the code book being used by base station and at least one terminal of MIMO communication system is provided, wherein, described code book comprises a plurality of code word matrix C _1,1, C _2,1, C _3,1, C _4,1, C _5,1, C _6,1, C _7,1, C _8,1, C _9,1, C _10,1, C _11,1, C _12,1, C _13,1, C _14,1, C _15,1and C _16,1, by a plurality of code word matrix described in lower table definition:

In another general aspect, a kind of method for precoding of the base station for Single User MIMO communication system, described method comprises: reference to storage, described memory stores comprise a plurality of code word matrix C of 4 * 1 _1,1, C _2,1, C _3,1, C _4,1, C _5,1, C _6,1, C _7,1, C _8,1, C _9,1, C _10,1, C _11,1, C _12,1, C _13,1, C _14,1, C _15,1and C _16,1code book; Use described code book to the data flow being sent out is carried out to precoding, wherein, by a plurality of code word matrix described in lower table definition:

Described precoding step comprises: at least one code word matrix based in described a plurality of code word matrix is calculated pre-coding matrix; Use pre-coding matrix to carry out precoding to data stream.

Described method also can comprise: from terminal receiving feedback information, wherein, described precoding step can comprise: with feedback information and described code book, data stream is carried out to precoding.

In another general aspect, a kind of method for precoding of the base station for multi-user MIMO communication system comprises: reference to storage, described memory stores comprise a plurality of code word matrix C of 4 * 1 _1,1, C _2,1, C _3,1, C _4,1, C _5,1, C _6,1, C _7,1, C _8,1, C _9,1, C _10,1, C _11,1, C _12,1, C _13,1, C _14,1, C _15,1and C _16,1code book; Use described code book to the data flow being sent out is carried out to precoding, wherein, by a plurality of code word matrix described in lower table definition:

In another general aspect, a kind of method of operation of the terminal for MIMO communication system comprises: reference to storage, described memory stores comprise a plurality of code word matrix C of 4 * 1 _1,1, C _2,1, C _3,1, C _4,1, C _5,1, C _6,1, C _7,1, C _8,1, C _9,1, C _10,1, C _11,1, C _12,1, C _13,1, C _14,1, C _15,1and C _16,1code book; The feedback information that preferred code word matrix with described a plurality of code word matrix is associated feeds back to base station, wherein, and by a plurality of code word matrix described in lower table definition:

Described method also can comprise: estimate the channel between base station and terminal; Channel based on estimating produces feedback information.

By the detailed description below in conjunction with the open exemplary embodiment of accompanying drawing, other features will be clearly for those skilled in the art.

Accompanying drawing explanation

Fig. 1 is the diagram that multiple-input and multiple-output (MIMO) communication system according to exemplary embodiment is shown;

Fig. 2 is the block diagram illustrating according to the structure of the base station of exemplary embodiment;

Fig. 3 is the flow chart illustrating according to the MIMO communication means of exemplary embodiment;

Fig. 4 is the flow chart illustrating according to the MIMO communication means of another exemplary embodiment.

Run through accompanying drawing and detailed description, except as otherwise noted, identical Reference numeral should be understood to indicate similar elements, feature and structure.For clear and convenient, can amplify these elements.

Embodiment

Provide the following detailed description to contribute to reader to obtain the complete understanding of method described here, equipment and/or system.Therefore, various variations, modification and the equivalent of system described here, equipment and/or method can be provided for those of ordinary skills.For clearer and convenient, the description that can omit known function and structure.

Below, detailed description exemplary embodiment with reference to the accompanying drawings.

Fig. 1 illustrates the diagram of multiple-input and multiple-output (MIMO) communication system according to exemplary embodiment.Mimo system can be closed-loop MIMO communication system.

With reference to Fig. 1, MIMO communication system comprises base station 110 and a plurality of user (user 1, user 2, user n _u) 120,130 and 140.Although Fig. 1 shows the example of multi-user MIMO communication system, should understand disclosed system, equipment and/or method and can be applicable to Single User MIMO communication system.Here, term " closed loop " can represent a plurality of users (user 1, user 2, user n _u) 120,130 and 140 the feedback data that comprises channel information can be fed back to 110， base station, base station 110 and can produce signal transmission based on feedback data.In addition, except closed-loop MIMO communication system, according to after a while the code book of the exemplary embodiment of description being can be applicable to open loop MIMO communication system.Therefore, should understand exemplary embodiment and be not limited to closed-loop MIMO communication system.

A plurality of antennas can be installed in base station 110.Can be at user (user 1, user 2, user n _u) single or multiple antennas are installed in each in 120,130 and 140.Can be in base station 110 with user (user 1, user 2, user n _u) form channel between each in 120,130 and 140.Can pass through the channel sending and receiving signal of each formation.

Base station 110 can send to a plurality of users (user 1, user 2, user n by individual traffic or at least two data flow _u) 120,130 and 140.In this case, base station 110 can adopt space division multiple access (SDMA) scheme or SDM scheme.Base station 110 can be selected pre-coding matrix and use the pre-coding matrix of selecting to produce signal transmission from the matrix being included in code book.

For example, base station 110 can send to respectively a plurality of users (user 1, user 2, user n by pilot signal by down link _u) 120,130 and 140.Pilot signal is for base station 110 and a plurality of user (user 1, user 2, user n _u) 120,130 and 140 can be known.

With user (user 1, user 2, user n _u) each corresponding terminal in 120,130 and 140 can carry out and receive 110 known signals that send from base station, uses pilot signal to estimate in base station 110 and user (user 1, user 2, user n _u) channel that forms between each in 120,130 and 140, from least one matrix of codebook selecting or vector, and the information that joins of feedback and at least one matrix of selecting or vector correlation.Can carry out design codebooks according to the explanation of making to Fig. 4 with reference to Fig. 2 after a while.Can upgrade code book according to channel status.

Especially, user (user 1, user 2, user n _u) each pilot signal used in 120,130 and 140 estimates base station and user (user 1, user 2, user n _u) channel that forms between each in 120,130 and 140.User (user 1, user 2, user n _u) each in 120,130 and 140 can select any one vector as preferred vector, or from be included in the matrix code book, select any one matrix as preferred matrix from be included in the vector pre-stored code book.

For example, user (user 1, user 2, user n _u) each in 120,130 and 140 can be according to attainable data transmission rate or Signal Interference and Noise Ratio (SINR), from 2 ^bindividual vector or 2 ^bin individual matrix, select any one vector or any one matrix as preferred vector or preferred matrix.Here, B represents the quantity of feedback bits.User (user 1, user 2, user n _u) each in 120,130 and 140 can determine the preferred transmission rank (transmission rank) of oneself.Transmission rank can be corresponding to the quantity of data flow.

User (user 1, user 2, user n _u) 120,130 with in 140 each can by the preferred vector with selecting or preferably the associated information (following, to be called channel information) of matrix feed back to base station 110.Channel information can comprise channel condition information, channel quality information or channel directional information as used herein.

Base station 110 can receive user (user 1, user 2, user n _u) each channel information in 120,130 and 140, thereby determine pre-coding matrix.User (user 1, user 2, user n can for example, be selected according to various types of selection algorithms (, semi-orthogonal user selects (SUS) algorithm, greedy user to select (GUS) algorithm etc.) in base station 110 _u) part or all in 120,130 and 140.

Be stored in a plurality of users (user 1, user 2, user n _u) 120,130 can be stored in advance in base station 110 with the identical code book of code book in 140.(user 1, user 2, user n from a plurality of users can be used in base station 110 _u) 120,130 and 140 channel informations that feed back to, the matrix based on being included in pre-stored code book is determined pre-coding matrix.Base station 110 can determine that pre-coding matrix is to maximize total data transfer rate, that is, and and total speed.

Base station 110 can be based on definite pre-coding matrix to data flow S ₁and S ₂carry out precoding, thereby produce signal transmission.The processing that produces signal transmission by base station 110 is called as " beam forming ".

Base station 110 and a plurality of users (user 1, user 2, user n _u) channel circumstance between 120,130 and 140 can be variable.In base station 110 and a plurality of user (user 1, user 2, user n _u) 120,130 and 140 use in the situation of fixed codebooks, be difficult to coordinate with the channel circumstance changing adaptively.Although will describe after a while base station 110 and a plurality of user (user 1, user 2, user n in detail _uthereby) 120,130 and 140 can be adaptively coordinate to upgrade code book with the channel circumstance changing.

Base station 110 can produce new pre-coding matrix.Particularly, base station 110 can be used the code book of renewal that previous pre-coding matrix is updated to new pre-coding matrix.

Fig. 2 illustrates according to the structure of the base station of exemplary embodiment.

With reference to Fig. 2, according to the base station of exemplary embodiment, comprise layer map unit 210, MIMO coding unit 220, precoder 230 and N _t individual entity antenna 240.

At least one code word at least one user can be mapped at least one layer.Dimension at code word x is N _cin * 1 situation, layer map unit 210 can be used has N _s* N _cthe matrix P of dimension is mapped at least one layer by code word x.Here, N _sthe quantity that represents the number of plies or effective antenna.Therefore, can obtain following equation 1:

s＝Px (1)。

MIMO coding unit 220 can be used has N _s* N _sthe matrix function M of dimension carries out space-time modulation to S.MIMO coding unit 220 can be carried out space-frequency piece coding, spatial reuse etc. according to transmission rank.

Precoder 230 can carry out precoding to output (that is, the data flow of MIMO coding unit 220), thereby produces the signal transmission sending by entity antenna 240.Dimension or the quantity of output (that is, the data flow of MIMO coding unit 220) can be indicated transmission rank.Precoder 230 can be used has N _t* N _sthe pre-coding matrix U of dimension produces signal transmission.Therefore, can obtain following equation 2:

z＝UM(s) (2)。

Below, W represents pre-coding matrix, and R represents the quantity of transmission rank or effective antenna.Here, the dimension of pre-coding matrix W is N _t* R.In MIMO coding unit 220 usage spaces, multiplexing in the situation that, can provide Z by following equation 3:

$z=\mathrm{WB}=\left[\begin{array}{cc}{u}_{11}& u_{1R}\\ -& -\\ -& -\\ -& -\\ u_{\mathrm{Nt}1}& u_{\mathrm{NtR}}\end{array}\right]\left[\begin{array}{c}{s}_1\\ -\\ -\\ -\\ s_R\end{array}\right]---\left(3\right).$

With reference to above-mentioned equation 3, pre-coding matrix W also can be called as weighting matrix.Can determine according to the quantity of transmission rank and entity antenna the dimension of pre-coding matrix W.For example,, at the quantity N of entity antenna _t4 and transmission rank is, in 2 situation, can provide pre-coding matrix W by following equation 4:

$W=\left[\begin{array}{cc}{W}_{11}& W_{12}\\ W_{21}& W_{22}\\ W_{31}& W_{32}\\ W_{41}& W_{42}\end{array}\right]---\left(4\right).$

code book attribute

The code book using in closed-loop MIMO communication system or open loop MIMO communication system can comprise a plurality of matrixes or a plurality of vector.A plurality of matrixes or a plurality of vector that can comprise based on code book are determined pre-coding matrix or precoding vector.Therefore, need design codebooks well.

1) in the situation that the quantity of the entity antenna of base station is two code books that use in the down link of Single User MIMO communication system:

For example, in the situation that the quantity of the entity antenna of base station is two, according to the code book using in Single User MIMO communication system of exemplary embodiment, can be designed to provide by following equation 5:

${\mathrm{<figure-callout\; id="1"\; label="W"\; filenames="HPA00001280680200011.png"\; state="\{\{state\}\}">W</figure-callout>}}_1=\frac{1}{\sqrt{2}}*\left[\begin{array}{cc}1& 1\\ 1& -1\end{array}\right],$

$W_2=\frac{1}{\sqrt{2}}*\left[\begin{array}{cc}1& 1\\ j& -j\end{array}\right],$

$W_3=\left[\begin{array}{cc}1& 0\\ 0& \frac{1+j}{\sqrt{2}}\end{array}\right]*{\mathrm{<figure-callout\; id="1"\; label="W"\; filenames="HPA00001280680200011.png"\; state="\{\{state\}\}">W</figure-callout>}}_1=\frac{1}{\sqrt{2}}\left[\begin{array}{cc}1& 1\\ \frac{1+j}{\sqrt{2}}& \frac{-1-j}{\sqrt{2}}\end{array}\right],$

$W_4=\left[\begin{array}{cc}1& 0\\ 0& \frac{1+j}{\sqrt{2}}\end{array}\right]*W_2=\frac{1}{\sqrt{2}}\left[\begin{array}{cc}1& 1\\ \frac{-1+j}{\sqrt{2}}& \frac{1-j}{\sqrt{2}}\end{array}\right]---\left(5\right).$

In this example, the matrix or the vector that are included in for the code book of Single User MIMO communication system can be confirmed as providing by following table 1:

Table 1

Send code book index	Transmission rank	1	Transmission rank 2
				1	C 1，1＝W1(；，1)	C 1，2＝W1(；，12)
2	C 2，1＝W1(；，2)	C 2，2＝W2(；，12)
			3	C 3，1＝W2(；，1)	C 3，2＝W3(；，12)
4	C 4，1＝W2(；，2)	C 4，2＝W4(；，12)
			5	C 5，1＝W3(；，1)	n/a
6	C 6，1＝W3(；，2)	n/a
			7	C 7，1＝W4(；，1)	n/a
8	C 8，1＝W4(；，2)	n/a

With reference to above table 1, W _k(; , n) represent W _kn column vector, W _k(; , n m) and represent to comprise W _kn column vector and the matrix of m column vector.In the situation that transmission rank is 1, pre-coding matrix can be W ₁(; , 1), W ₁(; , 2), W ₂(; , 1), W ₂(; , 2), W ₃(; , 1), W ₃(; , 2), W ₄(; , 1) and W ₄(; , 2) in any one.In the situation that transmission rank is 2, pre-coding matrix can be W ₁(; , 1 2), W ₂(; , 1 2), W ₃(; , 1 2) and W ₄(; , 1 2) in any one.

2) in the situation that the quantity of the entity antenna of base station is two code books that use in the down link of multi-user MIMO communication system of carrying out unitary matrice precoding (unitary precoding):

For example, in the situation that the quantity of the entity antenna of base station is two, according to the code book using in the down link of multi-user MIMO communication system of exemplary embodiment, can be designed to provide by following equation 6:

${\mathrm{<figure-callout\; id="1"\; label="W"\; filenames="HPA00001280680200011.png"\; state="\{\{state\}\}">W</figure-callout>}}_1=\frac{1}{\sqrt{2}}*\left[\begin{array}{cc}1& 1\\ 1& -1\end{array}\right]$

$W_2=\frac{1}{\sqrt{2}}*\left[\begin{array}{cc}1& 1\\ j& -j\end{array}\right]---\left(6\right).$

For carrying out the vector that the code book of multi-user MIMO communication system of unitary matrice precoding comprises, can be confirmed as providing by following table 2:

Table 2

The vector using in above table 2 can be in terminal for channel quantitative.Can be given in base station for the matrix of precoding by above equation 6.

With reference to above table 2, in the situation that transmission rank is 1, can be by suitably combining W ₁(; , 1), W ₁(; , 2), W ₂(; , 1) and W ₂(; , 2) and build pre-coding matrix.Here, W _k(; , n) represent W _kn column vector.

In the situation that multi-user MIMO communication system is carried out non-unitary matrice coding, the code book for channel quantitative using in terminal is identical with order 1 code book using in Single User MIMO communication system.Therefore,, in the situation that multi-user MIMO communication system is carried out non-unitary matrice precoding, code book can comprise the W being contained in above equation 5 ₁(; , 1), W ₁(; , 2), W ₂(; , 1), W ₂(; , 2), W ₃(; , 1), W ₃(; , 2), W ₄(; , 1) and W ₄(; , 2).Base station can only be used the subset of code book for this order 1 Single User MIMO communication system.

3) in the situation that the quantity of the entity antenna of base station is the first example of four code books that use in the down link of Single User MIMO communication system or multi-user MIMO communication system:

3-1) in the situation that the quantity of the entity antenna of base station is four code books that use in the down link of Single User MIMO communication system:

For example, in the situation that the quantity of the entity antenna of base station is four, according to the code book using in the down link of Single User MIMO communication system of exemplary embodiment, can be designed to be provided by following equation 7:

${\mathrm{<figure-callout\; id="1"\; label="W"\; filenames="HPA00001280680200011.png"\; state="\{\{state\}\}">W</figure-callout>}}_1=\frac{1}{\sqrt{2}}*U_{\mathrm{rot}}*\left[\begin{array}{cccc}1& 1& 0& 0\\ 1& -1& 0& 0\\ 0& 0& 1& 1\\ 0& 0& 1& -1\end{array}\right],$

$W_2=\frac{1}{\sqrt{2}}*U_{\mathrm{rot}}*\left[\begin{array}{cccc}1& 1& 0& 0\\ j& -j& 0& 0\\ 0& 0& 1& 1\\ 0& 0& j& -j\end{array}\right],$

$W_3=\frac{1}{\sqrt{2}}*U_{\mathrm{rot}}*\left[\begin{array}{cccc}1& 1& 0& 0\\ 1& -1& 0& 0\\ 0& 0& 1& 1\\ 0& 0& j& -j\end{array}\right],$

$W_4=\frac{1}{\sqrt{2}}*U_{\mathrm{rot}}*\left[\begin{array}{cccc}1& 1& 0& 0\\ j& -j& 0& 0\\ 0& 0& 1& 1\\ 0& 0& 1& -1\end{array}\right],$

$W_5=\mathrm{diag}(\mathrm{1,1,1},-1)*\mathrm{DFT}=0.5*\left[\begin{array}{cccc}1& 1& 1& 1\\ 1& j& -1& -j\\ 1& -1& 1& -1\\ -1& j& 1& -j\end{array}\right],$

$W_6=\mathrm{diag}(1,\frac{(1+j)}{\sqrt{2}},j,\frac{(-1+j)}{\sqrt{2}})*\mathrm{DFT}=0.5*\left[\begin{array}{cccc}1& 1& 1& 1\\ \frac{(1+j)}{\sqrt{2}}& \frac{(-1+j)}{\sqrt{2}}& \frac{(-1-j)}{\sqrt{2}}& \frac{(1-j)}{\sqrt{2}}\\ j& -j& j& -j\\ \frac{(-1+j)}{\sqrt{2}}& \frac{(1+j)}{\sqrt{2}}& \frac{(1-j)}{\sqrt{2}}& \frac{(-1-j)}{\sqrt{2}}\end{array}\right]---\left(7\right).$

Here, spin matrix is

$U_{\mathrm{rot}}=\frac{1}{\sqrt{2}}\left[\begin{array}{cccc}1& 0& -1& 0\\ 0& 1& 0& -1\\ 1& 0& 1& 0\\ 0& 1& 0& 1\end{array}\right],$

Quadrature Phase Shift Keying (QPSK) discrete Fourier transform (DFT) (DFT) matrix is

$\mathrm{DFT}=0.5*\left[\begin{array}{cccc}1& 1& 1& 1\\ 1& j& -1& -j\\ 1& -1& 1& -1\\ 1& -j& -1& j\end{array}\right],$

Diag (a, b, c, d) is 4 * 4 matrixes, and the diagonal element of diag (a, b, c, d) is a, b, c, d, and remaining element is zero.

Can determine and be included in the matrix for the code book of Single User MIMO communication system according to transmission rank, by following table 3, be provided:

Table 3

With reference to above table 3, in the situation that transmission rank is 4, based on W ₁(; , 123 4), W ₂(; , 123 4), W ₃(; , 123 4), W ₄(; , 123 4), W ₅(; , 123 4) and W ₆(; , 123 4) in any one produce pre-coding matrix.Here, W _k(; , n m o p) and represent to comprise W _kthe matrix of n column vector, m column vector, o column vector and p column vector.

In the situation that transmission rank is 3, can be based on W ₁(; , 12 3), W ₁(; , 12 4), W ₁(; , 13 4), W ₁(; , 2 34), W ₂(; , 12 3), W ₂(; , 12 4), W ₂(; , 13 4), W ₂(; , 23 4), W ₃(; , 12 3), W ₃(; , 13 4), W ₄(; , 12 3), W ₄(; , 13 4), W ₅(; , 12 3), W ₅(; , 13 4), W ₆(; , 12 4) and W ₆(; , 23 4) in any one produce pre-coding matrix.Here, W _k(; , n m o) and represent to comprise W _kthe matrix of n column vector, m column vector and o column vector.

In the situation that transmission rank is 2, can be based on W ₁(; , 1 2), W ₁(; , 1 3), W ₁(; , 1 4), W ₁(; , 2 3), W ₁(; , 2 4), W ₁(; , 3 4), W ₂(; , 1 3), W ₂(; , 1 4), W ₂(; , 2 3), W ₂(; , 2 4), W ₃(; , 1 3), W ₃(; , 1 4), W ₄(; , 13), W ₄(; , 1 4), W ₅(; , 1 3) and W ₆(; , 2 4) in any one produce pre-coding matrix.Here, W _k(; , n m) and represent to comprise W _kn column vector and the matrix of m column vector.

In the situation that transmission rank is 1, can be based on W ₁(; , 2), W ₁(; , 3), W ₁(; , 4), W ₂(; , 2), W ₂(; , 3), W ₂(; , 4), W ₃(; , 1), W ₄(; , 1), W ₅(; , 1), W ₅(; , 2), W ₅(; , 3), W ₅(; , 4), W ₆(; , 1), W ₆(; , 2), W ₆(; , 3) and W ₆(; , 4) in any one produce pre-coding matrix.Here, W _k(; , n) represent to comprise W _kthe matrix of n column vector.

The code word being included in above table 3 can be represented as follows:

C _1，1＝

0.5000

-0.5000

0.5000

-0.5000

C _2，1＝

-0.5000

-0.5000

0.5000

0.5000

C _3，1＝

-0.5000

0.5000

0.5000

-0.5000

C _4，1＝

0.5000

0-0.5000i

0.5000

0-0.5000i

C _5，1＝

-0.5000

0-0.5000i

0.5000

0+0.5000i

C _6，1＝

-0.5000

0+0.5000i

0.5000

0-0.5000i

C _7，1＝

0.5000

0.5000

0.5000

0.5000

C _8，1＝

0.5000

0+0.5000i

0.5000

0+0.5000i

C _9，1＝

0.5000

0.5000

0.5000

-0.5000

C _10，1＝

0.5000

0+0.5000i

-0.5000

0+0.5000i

C _11，1＝

0.5000

-0.5000

0.5000

0.5000

C _12，1＝

0.5000

0-0.5000i

-0.5000

0-0.5000i

C _13，1＝

0.5000

0.3536+0.3536i

0+0.5000i

-0.3536+0.3536i

C _14，1＝

0.5000

-0.3536+0.3536i

0-0.5000i

0.3536+0.3536i

C _15，1＝

0.5000

-0.3536-0.3536i

0+0.5000i

0.3536-0.3536i

C _16，1＝

0.5000

0.3536-0.3536i

0-0.5000i

-0.3536-0.3536i

C _1，2＝

0.5000 0.5000

0.5000 -0.5000

0.5000 0.5000

0.5000 -0.5000

C _2，2＝

0.5000 -0.5000

0.5000 -0.5000

0.5000 0.5000

0.5000 0.5000

C _3，2＝

0.5000 -0.5000

0.5000 0.5000

0.5000 0.5000

0.5000 -0.5000

C _4，2＝

0.5000 -0.5000

-0.5000 -0.5000

0.5000 0.5000

-0.5000 0.5000

C _5，2＝

0.5000 -0.5000

-0.5000 0.5000

0.5000 0.5000

-0.5000 -0.5000

C _6，2＝

-0.5000 -0.5000

-0.5000 0.5000

0.5000 0.5000

0.5000 -0.5000

C _7，2＝

0.5000 -0.5000

0+0.5000i 0-0.5000i

0.5000 0.5000

0+0.5000i 0+0.5000i

C _8，2＝

0.5000 -0.5000

0+0.5000i 0+0.5000i

0.5000 0.5000

0+0.5000i 0-0.5000i

C _9，2＝

0.5000 -0.5000

0-0.5000i 0-0.5000i

0.5000 0.5000

0-0.5000i 0+0.5000i

C _10，2＝

0.5000 -0.5000

0-0.5000i 0+0.5000i

0.5000 0.5000

0-0.5000i 0-0.5000i

C _11，2＝

0.5000 -0.5000

0.50000 -0.5000i

0.5000 0.5000

0.5000 0+0.5000i

C _12，2＝

0.5000 -0.5000

0.50000 +0.5000i

0.5000 0.5000

0.50000 -0.5000i

C _13，2＝

0.5000 -0.5000

0+0.5000i -0.5000

0.5000 0.5000

0+0.5000i 0.5000

C _14，2＝

0.5000 -0.5000

0+0.5000i 0.5000

0.5000 0.5000

0+0.5000i -0.5000

C _15，2＝

0.5000 0.5000

0.5000 -0.5000

0.5000 0.5000

-0.5000 0.5000

C _16，2＝

0.5000 0.5000

-0.3536+0.3536i 0.3536-0.3536i

0-0.5000i 0-0.5000i

0.3536+0.3536i -0.3536-0.3536i

C _1，3＝

0.5000 0.5000 -0.5000

0.5000 -0.5000 -0.5000

0.5000 0.5000 0.5000

0.5000 -0.5000 0.5000

C _2，3＝

0.5000 0.5000 -0.5000

0.5000 -0.5000 0.5000

0.5000 0.5000 0.5000

0.5000 -0.5000 -0.5000

C _3，3＝

0.5000 -0.5000 -0.5000

0.5000 -0.5000 0.5000

0.5000 0.5000 0.5000

0.5000 0.5000 -0.5000

C _4，3＝

0.5000 -0.5000 -0.5000

-0.5000 -0.5000 0.5000

0.5000 0.5000 0.5000

-0.5000 0.5000 -0.5000

C _5，3＝

0.5000 0.5000 -0.5000

0+0.5000i 0-0.5000i 0-0.5000i

0.5000 0.5000 0.5000

0+0.5000i 0-0.5000i 0+0.5000i

C _6，3＝

0.5000 0.5000 -0.5000

0+0.5000i 0-0.5000i 0+0.5000i

0.5000 0.5000 0.5000

0+0.5000i 0-0.5000i 0-0.5000i

C _7，3＝

0.5000 -0.5000 -0.5000

0+0.5000i 0-0.5000i 0+0.5000i

0.5000 0.5000 0.5000

0+0.5000i 0+0.5000i 0-0.5000i

C _8，3＝

0.5000 -0.5000 -0.5000

0-0.5000i 0-0.5000i 0+0.5000i

0.5000 0.5000 0.5000

0-0.5000i 0+0.5000i 0-0.5000i

C _9，3＝

0.5000 0.5000 -0.5000

0.5000 -0.50000 -0.5000i

0.5000 0.5000 0.5000

0.5000 -0.50000 +0.5000i

C _10，3＝

0.5000 -0.5000 -0.5000

0.50000 -0.5000i 0+0.5000i

0.5000 0.5000 0.5000

0.50000 +0.5000i 0-0.5000i

C _11，3＝

0.5000 0.5000 -0.5000

0+0.5000i 0-0.5000i -0.5000

0.5000 0.5000 0.5000

0+0.5000i 0-0.5000i 0.5000

C _12，3＝

0.5000 -0.5000 -0.5000

0+0.5000i -0.5000 0.5000

0.5000 0.5000 0.5000

0+0.5000i 0.5000 -0.5000

C _13，3＝

0.5000 0.5000 0.5000

0.50000 +0.5000i -0.5000

0.5000 -0.5000 0.5000

-0.5000 0+0.5000i 0.5000

C _14，3＝

0.5000 0.5000 0.5000

0.5000 -0.50000 -0.5000i

0.5000 0.5000 -0.5000

-0.5000 0.50000 -0.5000i

C _15，3＝

0.5000 0.5000 0.5000

0.3536+0.3536i -0.3536+0.3536i 0.3536-0.3536i

0+0.5000i 0-0.5000i 0-0.5000i

-0.3536+0.3536i 0.3536+0.3536i -0.3536-0.3536i

C _16，3＝

0.5000 0.5000 0.5000

-0.3536+0.3536i -0.3536-0.3536i 0.3536-0.3536i

0-0.5000i 0+0.5000i 0-0.5000i

0.3536+0.3536i 0.3536-0.3536i -0.3536-0.3536i

C _1，4＝

0.5000 0.5000 -0.5000 -0.5000

0.5000 -0.5000 -0.5000 0.5000

0.5000 0.5000 0.5000 0.5000

0.5000 -0.5000 0.5000 -0.5000

C _2，4＝

0.5000 0.5000 -0.5000 -0.5000

0+0.5000i 0-0.5000i 0-0.5000i 0+0.5000i

0.5000 0.5000 0.5000 0.5000

0+0.5000i 0-0.5000i 0+0.5000i 0-0.5000i

C _3，4＝

0.5000 0.5000 -0.5000 -0.5000

0.5000 -0.50000 -0.5000i 0+0.5000i

0.5000 0.5000 0.5000 0.5000

0.5000 -0.5000 0+0.5000i 0-0.5000i

C _4，4＝

0.5000 0.5000 -0.5000 -0.5000

0+0.5000i 0-0.5000i -0.5000 0.5000

0.5000 0.5000 0.5000 0.5000

0+0.5000i 0-0.5000i 0.5000 -0.5000

C _5，4＝

0.5000 0.5000 0.5000 0.5000

0.5000 0+0.5000i -0.50000 -0.5000i

0.5000 -0.5000 0.5000 -0.5000

-0.5000 0+0.5000i 0.50000 -0.5000i

C _6，4＝

0.5000 0.5000 0.5000 0.5000

0.3536+0.3536i -0.3536+0.3536i -0.3536-0.3536i 0.3536-0.3536i

0+0.5000i 0-0.5000i 0+0.5000i 0-0.5000i

-0.3536+0.3536i 0.3536+0.3536i 0.3536-0.3536i -0.3536-0.3536i

3-2) in the situation that the quantity of the entity antenna of base station is four code books that use in the down link of multi-user MIMO communication system of carrying out unitary matrice precoding:

For example, in the situation that the quantity of the entity antenna of base station is four, can use the code book of the use in the down link of multi-user MIMO communication system of following equation 8 design consideration exemplary embodiments:

$W_3=\frac{1}{\sqrt{2}}*U_{\mathrm{rot}}*\left[\begin{array}{cccc}1& 1& 0& 0\\ 1& -1& 0& 0\\ 0& 0& 1& 1\\ 0& 0& j& -j\end{array}\right]$

$W_6=\mathrm{diag}(1,\frac{(1+j)}{\sqrt{2}},j,\frac{(-1+j)}{\sqrt{2}})*\mathrm{DFT}=0.5*\left[\begin{array}{cccc}1& 1& 1& 1\\ \frac{(1+j)}{\sqrt{2}}& \frac{(-1+j)}{\sqrt{2}}& \frac{(-1-j)}{\sqrt{2}}& \frac{(1-j)}{\sqrt{2}}\\ j& -j& j& -j\\ \frac{(-1+j)}{\sqrt{2}}& \frac{(1+j)}{\sqrt{2}}& \frac{(1-j)}{\sqrt{2}}& \frac{(-1-j)}{\sqrt{2}}\end{array}\right]---\left(8\right).$

Can provide for carrying out the included code word of code book of the multi-user MIMO communication system of unitary matrice precoding by following table 4:

Table 4

Send code book index	The code word for quantizing of using in terminal
		1	M 1＝W3(；，1)
2	M 2＝W3(；，2)
		3	M 3＝W3(；，3)
4	M 4＝W3(；，4)
		5	M 5＝W6(；，1)
6	M 6＝W6(；，2)
		7	M 7＝W6(；，3)
8	M 8＝W6(；，4)

With reference to above table 4, in the situation that each user's transmission rank is 1, can be by suitably combining W ₃(; , 1), W ₃(; , 2), W ₃(; , 3), W ₃(; , 4), W ₆(; , 1), W ₆(; , 2), W ₆(; , 3) and W ₆(; , 4) and build pre-coding matrix.Here, W _k(; , n) represent W _kn column vector.

The code word being included in above table 4 can be expressed as followsin:

M ₁＝

0.5000

0.5000

0.5000

0.5000

M ₂＝

0.5000

-0.5000

0.5000

-0.5000

M ₃＝

-0.5000

0-0.5000i

0.5000

0+0.5000i

M ₄＝

-0.5000

0+0.5000i

0.5000

0-0.5000i

M ₅＝

0.5000

0.3536+0.3536i

0+0.5000i

-0.3536+0.3536i

M ₆＝

0.5000

-0.3536+0.3536i

0-0.5000i

0.3536+0.3536i

M ₇＝

0.5000

-0.3536-0.3536i

0+0.5000i

0.3536-0.3536i

M ₈＝

0.5000

0.3536-0.3536i

0-0.5000i

-0.3536-0.3536i

3-3) in the situation that the quantity of the entity antenna of base station is four code books that use in the down link of multi-user MIMO communication system of carrying out non-unitary matrice precoding:

For example, can provide included code word in the code book using in the down link of the multi-user MIMO communication system of carrying out non-unitary matrice precoding by following table 5.Here, in multi-user MIMO communication system, each user's order is 1:

Table 5

Send code book index	Order	1
			1	C 1，1＝W1(；，2)
2	C 2，1＝W1(；，3)
		3	C 3，1＝W1(；，4)
4	C 4，1＝W2(；，2)
		5	C 5，1＝W2(；，3)
6	C 6，1＝W2(；，4)
		7	C 7，1＝W3(；，1)
8	C 8，1＝W4(；，1)
		9	C 9，1＝W5(；，1)
10	C 10，1＝W5(；，2)
		11	C 11，1＝W5(；，3)
12	C 12，1＝W5(；，4)
		13	C 13，1＝W6(；，1)
14	C 14，1＝W6(；，2)
		15	C 15，1＝W6(；，3)
16	C 16，1＝W6(；，4)

The code word being included in above table 5 can be represented as follows:

C _1，1＝

0.5000

-0.5000

0.5000

-0.5000

C _2，1＝

-0.5000

-0.5000

0.5000

0.5000

C _3，1＝

-0.5000

0.5000

0.5000

-0.5000

C _4，1＝

0.5000

0-0.5000i

0.5000

0-0.5000i

C _5，1＝

-0.5000

0-0.5000i

0.5000

0+0.5000i

C _6，1＝

-0.5000

0+0.5000i

0.5000

0-0.5000i

C _7，1＝

0.5000

0.5000

0.5000

0.5000

C _8，1＝

0.5000

0+0.5000i

0.5000

0+0.5000i

C _9，1＝

0.5000

0.5000

0.5000

-0.5000

C _10，1＝

0.5000

0+0.5000i

-0.5000

0+0.5000i

C _11，1＝

0.5000

-0.5000

0.5000

0.5000

C _12，1＝

0.5000

0-0.5000i

-0.5000

0-0.5000i

C _13，1＝

0.5000

0.3536+0.3536i

0+0.5000i

-0.3536+0.3536i

C _14，1＝

0.5000

-0.3536+0.3536i

0-0.5000i

0.3536+0.3536i

C _15，1＝

0.5000

-0.3536-0.3536i

0+0.5000i

0.3536-0.3536i

C _16，1＝

0.5000

0.3536-0.3536i

0-0.5000i

-0.3536-0.3536i

4) in the situation that the quantity of the entity antenna of base station is the second example of four code books that use in the down link of Single User MIMO communication system or multi-user MIMO communication system:

4-1) in the situation that the quantity of the entity antenna of base station is four code books that use in the down link of Single User MIMO communication system:

Here, spin matrix Urot and QPSK DFT matrix can be defined as foloows:

$U_{\mathrm{rot}}=\frac{1}{\sqrt{2}}\left[\begin{array}{cccc}1& 0& -1& 0\\ 0& 1& 0& -1\\ 1& 0& 1& 0\\ 0& 1& 0& 1\end{array}\right],$

$\mathrm{DFT}=0.5*\left[\begin{array}{cccc}1& 1& 1& 1\\ 1& j& -1& -j\\ 1& -1& 1& -1\\ 1& -j& -1& j\end{array}\right],$

Diag (a, b, c, d) is 4 * 4 matrixes, and the diagonal element of diag (a, b, c, d) is a, b, c, d, and all the other all elements are zero.

Code word W ₁, W ₂, W ₃, W ₄, W ₅and W ₆can be defined as follows:

${\mathrm{<figure-callout\; id="1"\; label="W"\; filenames="HPA00001280680200011.png"\; state="\{\{state\}\}">W</figure-callout>}}_1=\frac{1}{\sqrt{2}}*U_{\mathrm{rot}}*\left[\begin{array}{cccc}1& 1& 0& 0\\ 1& -1& 0& 0\\ 0& 0& 1& 1\\ 0& 0& 1& -1\end{array}\right]*\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& -1& 0\\ 0& 0& 0& -1\end{array}\right]=0.5*\left[\begin{array}{cccc}1& 1& 1& 1\\ 1& -1& 1& -1\\ 1& 1& -1& -1\\ 1& -1& -1& 1\end{array}\right]$

$W_2=\frac{1}{\sqrt{2}}*U_{\mathrm{rot}}*\left[\begin{array}{cccc}1& 1& 0& 0\\ j& -j& 0& 0\\ 0& 0& 1& 1\\ 0& 0& j& -j\end{array}\right]*\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& -1& 0\\ 0& 0& 0& -1\end{array}\right]=0.5*\left[\begin{array}{cccc}1& 1& 1& 1\\ j& -j& j& -\mathrm{<figure-callout\; id="1"\; label="j"\; filenames="HPA00001280680200011.png"\; state="\{\{state\}\}">j</figure-callout>}\\ 1& 1& -1& -1\\ j& -j& -j& j\end{array}\right]$

$W_3=\frac{1}{\sqrt{2}}*U_{\mathrm{rot}}*\left[\begin{array}{cccc}1& 1& 0& 0\\ 1& -1& 0& 0\\ 0& 0& 1& 1\\ 0& 0& j& -j\end{array}\right]*\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& -1& 0\\ 0& 0& 0& -1\end{array}\right]=0.5*\left[\begin{array}{cccc}1& 1& 1& 1\\ 1& -1& j& -\mathrm{<figure-callout\; id="1"\; label="j"\; filenames="HPA00001280680200011.png"\; state="\{\{state\}\}">j</figure-callout>}\\ 1& 1& -1& -1\\ 1& -1& -j& j\end{array}\right]$

$W_4=\frac{1}{\sqrt{2}}*U_{\mathrm{rot}}*\left[\begin{array}{cccc}1& 1& 0& 0\\ j& -j& 0& 0\\ 0& 0& 1& 1\\ 0& 0& 1& -1\end{array}\right]*\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& -1& 0\\ 0& 0& 0& -1\end{array}\right]=0.5*\left[\begin{array}{cccc}1& 1& 1& 1\\ j& -j& 1& -1\\ 1& 1& -1& -1\\ j& -j& -1& 1\end{array}\right]$

$W_5=\mathrm{diag}(\mathrm{1,1,1},-1)*\mathrm{DFT}=0.5*\left[\begin{array}{cccc}1& 1& 1& 1\\ 1& j& -1& -j\\ 1& -1& 1& -1\\ -1& j& 1& -j\end{array}\right]$

$W_6=\mathrm{diag}(1,\frac{(1+j)}{\sqrt{2}},j,\frac{(-1+j)}{\sqrt{2}})*\mathrm{DFT}=0.5*\left[\begin{array}{cccc}1& 1& 1& 1\\ \frac{(1+j)}{\sqrt{2}}& \frac{(-1+j)}{\sqrt{2}}& \frac{(-1-j)}{\sqrt{2}}& \frac{(1-j)}{\sqrt{2}}\\ j& -j& j& -j\\ \frac{(-1+j)}{\sqrt{2}}& \frac{(1+j)}{\sqrt{2}}& \frac{(1-j)}{\sqrt{2}}& \frac{(-1-j)}{\sqrt{2}}\end{array}\right]$

For example, in the situation that the quantity of the entity antenna of base station is four, according to the included matrix of the code book using in the down link of Single User MIMO communication system of the second example or code word, can be provided by following table 6:

Table 6

The code word being included in above table 6 can be expressed as followsin:

C _1，1＝

0.5000

-0.5000

0.5000

-0.5000

C _2，1＝

0.5000

0.5000

-0.5000

-0.5000

C _3，1＝

0.5000

-0.5000

-0.5000

0.5000

C _4，1＝

0.5000

0-0.5000i

0.5000

0-0.5000i

C _5，1＝

0.5000

0+0.5000i

-0.5000

0-0.5000i

C _6，1＝

0.5000

0-0.5000i

-0.5000

0+0.5000i

C _7，1＝

0.5000

0.5000

0.5000

0.5000

C _8，1＝

0.5000

0+0.5000i

0.5000

0+0.5000i

C _9，1＝

0.5000

0.5000

0.5000

-0.5000

C _10，1＝

0.5000

0+0.5000i

-0.5000

0+0.5000i

C _11，1＝

0.5000

-0.5000

0.5000

0.5000

C _12，1＝

0.5000

0-0.5000i

-0.5000

0-0.5000i

C _13，1＝

0.5000

0.3536+0.3536i

0+0.5000i

-0.3536+0.3536i

C _14，1＝

0.5000

-0.3536+0.3536i

0-0.5000i

0.3536+0.3536i

C _15，1＝

0.5000

-0.3536-0.3536i

0+0.5000i

0.3536-0.3536i

C _16，1＝

0.5000

0.3536-0.3536i

0-0.5000i

-0.3536-0.3536i

C _1，2＝

0.5000 0.5000

-0.5000 0.5000

0.5000 0.5000

-0.5000 0.5000

C _2，2＝

0.5000 0.5000

0.5000 0.5000

-0.5000 0.5000

-0.5000 0.5000

C _3，2＝

0.5000 0.5000

-0.5000 0.5000

-0.5000 0.5000

0.5000 0.5000

C _4，2＝

0.5000 0.5000

-0.5000 0.5000

0.5000 -0.5000

-0.5000 -0.5000

C _5，2＝

0.5000 0.5000

-0.5000 -0.5000

0.5000 -0.5000

-0.5000 0.5000

C _6，2＝

0.5000 0.5000

0.5000 -0.5000

-0.5000 -0.5000

-0.5000 0.5000

C _7，2＝

0.5000 0.5000

0+0.5000i 0+0.5000i

-0.5000 0.5000

0-0.5000i 0+0.5000i

C _8，2＝

0.5000 0.5000

0-0.5000i 0+0.5000i

-0.5000 0.5000

0+0.5000i 0+0.5000i

C _9，2＝

0.5000 0.5000

0-0.5000i 0+0.5000i

0.5000 -0.5000

0-0.5000i 0-0.5000i

C _10，2＝

0.5000 0.5000

0-0.5000i 0-0.5000i

0.5000 -0.5000

0-0.5000i 0+0.5000i

C _11，2＝

0.5000 0.5000

0+0.5000i 0.5000

-0.5000 0.5000

0-0.5000i 0.5000

C _12，2＝

0.5000 0.5000

0-0.5000i 0.5000

-0.5000 0.5000

0+0.5000i 0.5000

C _13，2＝

0.5000 0.5000

0.5000 0+0.5000i

-0.5000 0.5000

-0.5000 0+0.5000i

C _14，2＝

0.5000 0.5000

-0.5000 0+0.5000i

-0.5000 0.5000

0.5000 0+0.5000i

C _15，2＝

0.5000 0.5000

0.5000 -0.5000

0.5000 0.5000

-0.5000 0.5000

C _16，2＝

0.5000 0.5000

-0.3536+0.3536i 0.3536-0.3536i

0-0.5000i 0-0.5000i

0.3536+0.3536i -0.3536-0.3536i

C _1，3＝

0.5000 0.5000 0.5000

0.5000 -0.5000 0.5000

0.5000 0.5000 -0.5000

0.5000 -0.5000 -0.5000

C _2，3＝

0.5000 0.5000 0.5000

0.5000 -0.5000 -0.5000

0.5000 0.5000 -0.5000

0.5000 -0.5000 0.5000

C _3，3＝

0.5000 0.5000 0.5000

0.5000 0.5000 -0.5000

0.5000 -0.5000 -0.5000

0.5000 -0.5000 0.5000

C _4，3＝

0.5000 0.5000 0.5000

-0.5000 0.5000 -0.5000

0.5000 -0.5000 -0.5000

-0.5000 -0.5000 0.5000

C _5，3＝

0.5000 0.5000 0.5000

0+0.5000i 0-0.5000i 0+0.5000i

0.5000 0.5000 -0.5000

0+0.5000i 0-0.5000i 0-0.5000i

C _6，3＝

0.5000 0.5000 0.5000

0+0.5000i 0-0.5000i 0-0.5000i

0.5000 0.5000 -0.5000

0+0.5000i 0-0.5000i 0+0.5000i

C _7，3＝

0.5000 0.5000 0.5000

0+0.5000i 0+0.5000i 0-0.5000i

0.5000 -0.5000 -0.5000

0+0.5000i 0-0.5000i 0+0.5000i

C _8，3＝

0.5000 0.5000 0.5000

0-0.5000i 0+0.5000i 0-0.5000i

0.5000 -0.5000 -0.5000

0-0.5000i 0-0.5000i 0+0.5000i

C _9，3＝

0.5000 0.5000 0.5000

0.5000 0+0.5000i -0.5000

0.5000 -0.5000 0.5000

-0.5000 0+0.5000i 0.5000

C _10，3＝

0.5000 0.5000 0.5000

0.5000 0+0.5000i 0-0.5000i

0.5000 -0.5000 -0.5000

-0.50000 +0.5000i 0-0.5000i

C _11，3＝

0.5000 0.5000 0.5000

0.5000 -0.50000 -0.5000i

0.5000 0.5000 -0.5000

-0.5000 0.5000 0-0.5000i

C _12，3＝

0.5000 0.5000 0.5000

0+0.5000i -0.50000 -0.5000i

-0.5000 0.5000 -0.5000

0+0.5000i 0.5000 0-0.5000i

C _13，3＝

0.5000 0.5000 0.5000

0.3536+0.3536i -0.3536+0.3536i -0.3536-0.3536i

0+0.5000i 0-0.5000i 0+0.5000i

-0.3536+0.3536i 0.3536+0.3536i 0.3536-0.3536i

C _14.3＝

0.5000 0.5000 0.5000

0.3536+0.3536i -0.3536+0.3536i 0.3536-0.3536i

0+0.5000i 0-0.5000i 0-0.5000i

-0.3536+0.3536i 0.3536+0.3536i -0.3536-0.3536i

C _15，3＝

0.5000 0.5000 0.5000

0.3536+0.3536i -0.3536-0.3536i 0.3536-0.3536i

0+0.5000i 0+0.5000i 0-0.5000i

-0.3536+0.3536i 0.3536-0.3536i -0.3536-0.3536i

C _16，3＝

0.5000 0.5000 0.5000

-0.3536+0.3536i -0.3536-0.3536i 0.3536-0.3536i

0-0.5000i 0+0.5000i 0-0.5000i

0.3536+0.3536i 0.3536-0.3536i -0.3536-0.3536i

C _1，4＝

0.5000 0.5000 0.5000 0.5000

0.5000 -0.5000 0.5000 -0.5000

0.5000 0.5000 -0.5000 -0.5000

0.5000 -0.5000 -0.5000 0.5000

C _2，4＝

0.5000 0.5000 0.5000 0.5000

0+0.5000i 0-0.5000i 0+0.5000i 0-0.5000i

0.5000 0.5000 -0.5000 -0.5000

0+0.5000i 0-0.5000i 0-0.5000i 0+0.5000i

C _3，4＝

0.5000 0.5000 0.5000 0.5000

0.5000 -0.5000 0+0.5000i 0-0.5000i

0.5000 0.5000 -0.5000 -0.5000

0.5000 -0.5000 0-0.5000i 0+0.5000i

C _4，4＝

0.5000 0.5000 0.5000 0.5000

0+0.5000i 0-0.5000i 0.5000 -0.5000

0.5000 0.5000 -0.5000 -0.5000

0+0.5000i 0-0.5000i -0.5000 0.5000

C _5，4＝

0.5000 0.5000 0.5000 0.5000

0.5000 0+0.5000i -0.5000 0-0.5000i

0.5000 -0.5000 0.5000 -0.5000

-0.5000 0+0.5000i 0.50000 -0.5000i

C _6，4＝

0.5000 0.5000 0.5000 0.5000

0.3536+0.3536i -0.3536+0.3536i -0.3536-0.3536i 0.3536-0.3536i

0+0.5000i 0-0.5000i 0+0.5000i 0-0.5000i

-0.3536+0.3536i 0.3536+0.3536i 0.3536-0.3536i -0.3536-0.3536i

4-2) in the situation that the quantity of the entity antenna of base station is four code books that use in the down link of multi-user MIMO communication system of carrying out unitary matrice precoding:

For example, can be by suitably combining two following matrix W ₃and W ₆carry out the code book using in the down link of multi-user MIMO communication system of design consideration the second example:

$W_3=\frac{1}{\sqrt{2}}*U_{\mathrm{rot}}*\left[\begin{array}{cccc}1& 1& 0& 0\\ 1& -1& 0& 0\\ 0& 0& 1& 1\\ 0& 0& j& -j\end{array}\right]=0.5*\left[\begin{array}{cccc}1& 1& -1& -1\\ 1& -1& -\mathrm{<figure-callout\; id="1"\; label="j\; j"\; filenames="HPA00001280680200011.png"\; state="\{\{state\}\}">j</figure-callout>}& j\\ 1& 1& 1& 1\\ 1& -1& j& -j\end{array}\right]$

$W_6=\mathrm{diag}(1,\frac{(1+j)}{\sqrt{2}},j,\frac{(-1+j)}{\sqrt{2}})*\mathrm{DFT}=0.5*\left[\begin{array}{cccc}1& 1& 1& 1\\ \frac{(1+j)}{\sqrt{2}}& \frac{(-1+j)}{\sqrt{2}}& \frac{(-1-j)}{\sqrt{2}}& \frac{(1-j)}{\sqrt{2}}\\ j& -j& j& -j\\ \frac{(-1+j)}{\sqrt{2}}& \frac{(1+j)}{\sqrt{2}}& \frac{(1-j)}{\sqrt{2}}& \frac{(-1-j)}{\sqrt{2}}\end{array}\right]$

For example, in the situation that the quantity of the entity antenna of base station is four, can be provided according to the included matrix of the code book using in the down link of the multi-user MIMO communication system of the second example or code word by following table 7:

Table 7

Send code book index	Order	1
			1	M 1＝W3(；，1)
2	M 2＝W3(；，2)
		3	M 3＝W3(；，3)

4	M 4＝W3(；，4)
		5	M 5＝W6(；，1)
6	M 6＝W6(；，2)
		7	M 7＝W6(；，3)
8	M 8＝W6(；，4)

The code word being included in above table 7 can be expressed as followsin:

M ₁＝

0.5000

0.5000

0.5000

0.5000

M ₂＝

0.5000

-0.5000

0.5000

-0.5000

M ₃＝

-0.5000

0-0.5000i

0.5000

0+0.5000i

M ₄＝

-0.5000

0+0.5000i

0.5000

0-0.5000i

M ₅＝

0.5000

0.3536+0.3536i

0+0.5000i

-0.3536+0.3536i

M ₆＝

0.5000

-0.3536+0.3536i

0-0.5000i

0.3536+0.3536i

M ₇＝

0.5000

-0.3536-0.3536i

0+0.5000i

0.3536-0.3536i

M ₈＝

0.5000

0.3536-0.3536i

0-0.5000i

-0.3536-0.3536i

4-3) in the situation that the quantity of the entity antenna of base station is four code books that use in carrying out the down link of multi-user MIMO communication system of non-unitary matrice precoding:

For example, in the situation that the quantity of the entity antenna of base station is four, can provide the included code word of code book of using in the down link of the multi-user MIMO communication system of carrying out non-unitary matrice precoding by following table 8:

Table 8

Send code book index	Transmission rank	1
			1	C 1，1＝W1(；，2)
2	C 2，1＝W1(；，3)
		3	C 3，1＝W1(；，4)
4	C 4，1＝W2(；，2)
		5	C 5，1＝W2(；，3)
6	C 6，1＝W2(；，4)
		7	C 7，1＝W3(；，1)
8	C 8，1＝W4(；，1)
		9	C 9，1＝W5(；，1)
10	C 10，1＝W5(；，2)
		11	C 11，1＝W5(；，3)
12	C 12，1＝W5(；，4)
		13	C 13，1＝W6(；，1)

14	C 14，1＝W6(；，2)
		15	C 15，1＝W6(；，3)
16	C 16，1＝W6(；，4)

The code word being included in above table 8 can be expressed as followsin:

C _1，1＝

0.5000

-0.5000

0.5000

-0.5000

C _2，1＝

-0.5000

-0.5000

0.5000

0.5000

C _3，1＝

-0.5000

0.5000

0.5000

-0.5000

C _4，1＝

0.5000

0-0.5000i

0.5000

0-0.5000i

C _5，1＝

-0.5000

0-0.5000i

0.5000

0+0.5000i

C _6，1＝

-0.5000

0+0.5000i

0.5000

0-0.5000i

C _7，1＝

0.5000

0.5000

0.5000

0.5000

C _8，1＝

0.5000

0+0.5000i

0.5000

0+0.5000i

C _9，1＝

0.5000

0.5000

0.5000

-0.5000

C _10，1＝

0.5000

0+0.5000i

-0.5000

0+0.5000i

C _11，1＝

0.5000

-0.5000

0.5000

0.5000

C _12，1＝

0.5000

0-0.5000i

-0.5000

0-0.5000i

C _13，1＝

0.5000

0.3536+0.3536i

0+0.5000i

-0.3536+0.3536i

C _14，1＝

0.5000

-0.3536+0.3536i

0-0.5000i

0.3536+0.3536i

C _15，1＝

0.5000

-0.3536-0.3536i

0+0.5000i

0.3536-0.3536i

C _16，1＝

0.5000

0.3536-0.3536i

0-0.5000i

-0.3536-0.3536i

5) in the situation that the quantity of the entity antenna of base station is four, the 3rd example of the code book using in the down link of Single User MIMO communication system or multi-user MIMO communication system:

5-1) in the situation that the quantity of the entity antenna of base station is four code books that use in the down link of Single User MIMO communication system:

Here, spin matrix Urot and QPSK DFT matrix can be defined as foloows:

$U_{\mathrm{rot}}=\frac{1}{\sqrt{2}}\left[\begin{array}{cccc}1& 0& -1& 0\\ 0& 1& 0& -1\\ 1& 0& 1& 0\\ 0& 1& 0& 1\end{array}\right],$

$\mathrm{DFT}=0.5*\left[\begin{array}{cccc}1& 1& 1& 1\\ 1& j& -1& -j\\ 1& -1& 1& -1\\ 1& -j& -1& j\end{array}\right],$

Diag (a, b, c, d) is 4 * 4 matrixes, and the diagonal element of diag (a, b, c, d) is a, b, c, d, and all the other all elements are zero.

Code word W ₁, W ₂, W ₃, W ₄, W ₅and W ₆can be defined as follows:

${\mathrm{<figure-callout\; id="1"\; label="W"\; filenames="HPA00001280680200011.png"\; state="\{\{state\}\}">W</figure-callout>}}_1=\frac{1}{\sqrt{2}}*U_{\mathrm{rot}}*\left[\begin{array}{cccc}1& 1& 0& 0\\ 1& -1& 0& 0\\ 0& 0& 1& 1\\ 0& 0& 1& -1\end{array}\right]=0.5*\left[\begin{array}{cccc}1& 1& -1& -1\\ 1& -1& -1& 1\\ 1& 1& 1& 1\\ 1& -1& 1& -1\end{array}\right]$

$W_2=\frac{1}{\sqrt{2}}*U_{\mathrm{rot}}*\left[\begin{array}{cccc}1& 1& 0& 0\\ j& -j& 0& 0\\ 0& 0& 1& 1\\ 0& 0& j& -j\end{array}\right]=0.5*\left[\begin{array}{cccc}1& 1& -1& -1\\ j& -j& -\mathrm{<figure-callout\; id="1"\; label="j\; j"\; filenames="HPA00001280680200011.png"\; state="\{\{state\}\}">j</figure-callout>}& j\\ 1& 1& 1& 1\\ j& -j& j& -j\end{array}\right]$

$W_3=\frac{1}{\sqrt{2}}*U_{\mathrm{rot}}*\left[\begin{array}{cccc}1& 1& 0& 0\\ 1& -1& 0& 0\\ 0& 0& 1& 1\\ 0& 0& j& -j\end{array}\right]=0.5*\left[\begin{array}{cccc}1& 1& -1& -1\\ 1& -1& -\mathrm{<figure-callout\; id="1"\; label="j\; j"\; filenames="HPA00001280680200011.png"\; state="\{\{state\}\}">j</figure-callout>}& j\\ 1& 1& 1& 1\\ 1& -1& j& -j\end{array}\right]$

$W_4=\frac{1}{\sqrt{2}}*U_{\mathrm{rot}}*\left[\begin{array}{cccc}1& 1& 0& 0\\ j& -j& 0& 0\\ 0& 0& 1& 1\\ 0& 0& 1& -1\end{array}\right]=0.5*\left[\begin{array}{cccc}1& 1& -1& -1\\ j& -j& -1& 1\\ 1& 1& 1& 1\\ j& -j& 1& -1\end{array}\right]$

$W_5=\mathrm{diag}(\mathrm{1,1,1},-1)*\mathrm{DFT}=0.5*\left[\begin{array}{cccc}1& 1& 1& 1\\ 1& j& -1& -j\\ 1& -1& 1& -1\\ -1& j& 1& -j\end{array}\right]$

$W_6=\mathrm{diag}(1,\frac{(1+j)}{\sqrt{2}},j,\frac{(-1+j)}{\sqrt{2}})*\mathrm{DFT}=0.5*\left[\begin{array}{cccc}1& 1& 1& 1\\ \frac{(1+j)}{\sqrt{2}}& \frac{(-1+j)}{\sqrt{2}}& \frac{(-1-j)}{\sqrt{2}}& \frac{(1-j)}{\sqrt{2}}\\ j& -j& j& -j\\ \frac{(-1+j)}{\sqrt{2}}& \frac{(1+j)}{\sqrt{2}}& \frac{(1-j)}{\sqrt{2}}& \frac{(-1-j)}{\sqrt{2}}\end{array}\right]$

For example, in the situation that the quantity of the entity antenna of base station is four, according to the included matrix of the code book using in the down link of Single User MIMO communication system of the 3rd example or code word, can be provided by following table 9:

Table 9

The code word being included in above table 9 can be expressed as followsin:

C _1，1＝

0.5000

-0.5000

0.5000

-0.5000

C _2，1＝

-0.5000

-0.5000

0.5000

0.5000

C _3，1＝

-0.5000

0.5000

0.5000

-0.5000

C _4，1＝

0.5000

0-0.5000i

0.5000

0-0.5000i

C _5，1＝

-0.5000

0-0.5000i

0.5000

0+0.5000i

C _6，1＝

-0.5000

0+0.5000i

0.5000

0-0.5000i

C _7，1＝

0.5000

0.5000

0.5000

0.5000

C _8，1＝

0.5000

0+0.5000i

0.5000

0+0.5000i

C _9，1＝

0.5000

0.5000

0.5000

-0.5000

C _10，1＝

0.5000

0+0.5000i

-0.5000

0+0.5000i

C _11，1＝

0.5000

-0.5000

0.5000

0.5000

C _12，1＝

0.5000

0-0.5000i

-0.5000

0-0.5000i

C _13，1＝

0.5000

0.3536+0.3536i

0+0.5000i

-0.3536+0.3536i

C _14，1＝

0.5000

-0.3536+0.3536i

0-0.5000i

0.3536+0.3536i

C _15，1＝

0.5000

-0.3536-0.3536i

0+0.5000i

0.3536-0.3536i

C _16，1＝

0.5000

0.3536-0.3536i

0-0.5000i

-0.3536-0.3536i

C _1，2＝

0.5000 0.5000

0.5000 -0.5000

0.5000 0.5000

0.5000 -0.5000

C _2，2＝

0.5000 -0.5000

0.5000 -0.5000

0.5000 0.5000

0.5000 0.5000

C _3，2＝

0.5000 -0.5000

0.5000 0.5000

0.5000 0.5000

0.5000 -0.5000

C _4，2＝

0.5000 -0.5000

-0.5000 -0.5000

0.5000 0.5000

-0.5000 0.5000

C _5，2＝

0.5000 -0.5000

-0.5000 0.5000

0.5000 0.5000

-0.5000 -0.5000

C _6，2＝

-0.5000 -0.5000

-0.5000 0.5000

0.5000 0.5000

0.5000 -0.5000

C _7，2＝

0.5000 -0.5000

0+0.5000i 0-0.5000i

0.5000 0.5000

0+0.5000i 0+0.5000i

C _8，2＝

0.5000 -0.5000

0+0.5000i 0+0.5000i

0.5000 0.5000

0+0.5000i 0-0.5000i

C _9，2＝

0.5000- 0.5000

0-0.5000i 0-0.5000i

0.5000 0.5000

0-0.5000i 0+0.5000i

C _10，2＝

0.5000 -0.5000

0-0.5000i 0+0.5000i

0.5000 0.5000

0-0.5000i 0-0.5000i

C _11，2＝

0.5000 -0.5000

0.50000 -0.5000i

0.5000 0.5000

0.5000 0+0.5000i

C _12，2＝

0.5000 -0.5000

0.5000 0+0.5000i

0.5000 0.5000

0.5000 0-0.5000i

C _13，2＝

0.5000 -0.5000

0+0.5000i -0.5000

0.5000 0.5000

0+0.5000i 0.5000

C _14，2＝

0.5000 -0.5000

0+0.5000i 0.5000

0.5000 0.5000

0+0.5000i -0.5000

C _15，2＝

0.5000 0.5000

0.5000 -0.5000

0.5000 0.5000

-0.5000 0.5000

C _16，2＝

0.5000 0.5000

-0.3536+0.3536i 0.3536-0.3536i

0-0.5000i 0-0.5000i

0.3536+0.3536i -0.3536-0.3536i

C _1.3＝

0.5000 0.5000 -0.5000

0.5000 -0.5000 -0.5000

0.5000 0.5000 0.5000

0.5000 -0.5000 0.5000

C _2，3＝

0.5000 0.5000 -0.5000

0.5000 -0.5000 0.5000

0.5000 0.5000 0.5000

0.5000 -0.5000 -0.5000

C _3，3＝

0.5000 -0.5000 -0.5000

0.5000 -0.5000 0.5000

0.5000 0.5000 0.5000

0.5000 0.5000 -0.5000

C _4，3＝

0.5000 -0.5000 -0.5000

-0.5000 -0.5000 0.5000

0.5000 0.5000 0.5000

-0.5000 0.5000 -0.5000

C _5.3＝

0.5000 0.5000 -0.5000

0+0.5000i 0-0.5000i 0-0.5000i

0.5000 0.5000 0.5000

0+0.5000i 0-0.5000i 0+0.5000i

C _6，3＝

0.5000 0.5000 -0.5000

0+0.5000i 0-0.5000i 0+0.5000i

0.5000 0.5000 0.5000

0+0.5000i 0-0.5000i 0-0.5000i

C _7，3＝

0.5000 -0.5000 -0.5000

0+0.5000i 0-0.5000i 0+0.5000i

0.5000 0.5000 0.5000

0+0.5000i 0+0.5000i 0-0.5000i

C _8，3＝

0.5000 -0.5000 -0.5000

0-0.5000i 0-0.5000i 0+0.5000i

0.5000 0.5000 0.5000

0-0.5000i 0+0.5000i 0-0.5000i

C _9，3＝

0.5000 0.5000 0.5000

0.50000 +0.5000i -0.5000

0.5000 -0.5000 0.5000

-0.50000 +0.5000i 0.5000

C _10，3＝

0.5000 0.5000 0.5000

0.50000 +0.5000i 0-0.5000i

0.5000 -0.5000 -0.5000

-0.50000 +0.5000i 0-0.5000i

C _11，3＝

0.5000 0.5000 0.5000

0.5000 -0.50000 -0.5000i

0.5000 0.5000 -0.5000

-0.5000 0.50000 -0.5000i

C _12，3＝

0.5000 0.5000 0.5000

0+0.5000i -0.50000 -0.5000i

-0.5000 0.5000 -0.5000

0+0.5000i 0.5000 0-0.5000i

C _13，3＝

0.5000 0.5000 0.5000

0.3536+0.3536i -0.3536+0.3536i -0.3536-0.3536i

0+0.5000i 0-0.5000i 0+0.5000i

-0.3536+0.3536i 0.3536+0.3536i 0.3536-0.3536i

C _14，3＝

0.5000 0.5000 0.5000

0.3536+0.3536i -0.3536+0.3536i 0.3536-0.3536i

0+0.5000i 0-0.5000i 0-0.5000i

-0.3536+0.3536i 0.3536+0.3536i -0.3536-0.3536i

C _15，3＝

0.5000 0.5000 0.5000

0.3536+0.3536i -0.3536-0.3536i 0.3536-0.3536i

0+0.5000i 0+0.5000i 0-0.5000i

-0.3536+0.3536i 0.3536-0.3536i -0.3536-0.3536i

C _16，3＝

0.5000 0.5000 0.5000

-0.3536+0.3536i -0.3536-0.3536i 0.3536-0.3536i

0-0.5000i 0+0.5000i 0-0.5000i

0.3536+0.3536i 0.3536-0.3536i -0.3536-0.3536i

C _1，4＝

0.5000 0.5000 -0.5000 -0.5000

0.5000 -0.5000 -0.5000 0.5000

0.5000 0.5000 0.5000 0.5000

0.5000 -0.5000 0.5000 -0.5000

C _2，4＝

0.5000 0.5000 -0.5000 -0.5000

0+0.5000i 0-0.5000i 0-0.5000i 0+0.5000i

0.5000 0.5000 0.5000 0.5000

0+0.5000i 0-0.5000i 0+0.5000i 0-0.5000i

C _3，4＝

0.5000 0.5000 -0.5000 -0.5000

0.5000 -0.50000 -0.5000i 0+0.5000i

0.5000 0.5000 0.5000 0.5000

0.5000 -0.5000 0+0.5000i 0-0.5000i

C _4，4＝

0.5000 0.5000 -0.5000 -0.5000

0+0.5000i 0-0.5000i -0.5000 0.5000

0.5000 0.5000 0.5000 0.5000

0+0.5000i 0-0.5000i 0.5000 -0.5000

C _5，4＝

0.5000 0.5000 0.5000 0.5000

0.5000 0+0.5000i -0.5000 0-0.5000i

0.5000 -0.5000 0.5000 -0.5000

-0.5000 0+0.5000i 0.50000 -0.5000i

C _6，4＝

0.5000 0.5000 0.5000 0.5000

0.3536+0.3536i -0.3536+0.3536i -0.3536-0.3536i 0.3536-0.3536i

0+0.5000i 0-0.5000i 0+0.5000i 0-0.5000i

-0.3536+0.3536i 0.3536+0.3536i 0.3536-0.3536i -0.3536-0.3536i

5-2) in the situation that the quantity of the entity antenna of base station is four code books that use in the down link of multi-user MIMO communication system of carrying out unitary matrice precoding:

For example, can be by suitably combining two following matrix W ₃and W ₆carry out the code book using in the down link of multi-user MIMO communication system of design consideration the 3rd example:

$W_3=\frac{1}{\sqrt{2}}*U_{\mathrm{rot}}*\left[\begin{array}{cccc}1& 1& 0& 0\\ 1& -1& 0& 0\\ 0& 0& 1& 1\\ 0& 0& j& -j\end{array}\right]=0.5*\left[\begin{array}{cccc}1& 1& -1& -1\\ 1& -1& -\mathrm{<figure-callout\; id="1"\; label="j\; j"\; filenames="HPA00001280680200011.png"\; state="\{\{state\}\}">j</figure-callout>}& j\\ 1& 1& 1& 1\\ 1& -1& j& -j\end{array}\right]$

$W_6=\mathrm{diag}(1,\frac{(1+j)}{\sqrt{2}},j,\frac{(-1+j)}{\sqrt{2}})*\mathrm{DFT}=0.5*\left[\begin{array}{cccc}1& 1& 1& 1\\ \frac{(1+j)}{\sqrt{2}}& \frac{(-1+j)}{\sqrt{2}}& \frac{(-1-j)}{\sqrt{2}}& \frac{(1-j)}{\sqrt{2}}\\ j& -j& j& -j\\ \frac{(-1+j)}{\sqrt{2}}& \frac{(1+j)}{\sqrt{2}}& \frac{(1-j)}{\sqrt{2}}& \frac{(-1-j)}{\sqrt{2}}\end{array}\right]$

For example, in the situation that the quantity of the entity antenna of base station is four, can be provided according to the included matrix of the code book using in the down link of the multi-user MIMO communication system of the 3rd example or code word by following table 10:

Table 10

Send code book index	Order	1
			1	M 1＝W3(；，1)
2	M 2＝W3(；，2)
		3	M 3＝W3(；，3)
4	M 4＝W3(；，4)
		5	M 5＝W6(；，1)
6	M 6＝W6(；，2)
		7	M 7＝W6(；，3)
8	M 8＝W6(；，4)

The code word being included in above table 10 can be expressed as followsin:

M ₁＝

0.5000

0.5000

0.5000

0.5000

M ₂＝

0.5000

-0.5000

0.5000

-0.5000

M ₃＝

-0.5000

0-0.5000i

0.5000

0+0.5000i

M ₄＝

-0.5000

0+0.5000i

0.5000

0-0.5000i

M ₅＝

0.5000

0.3536+0.3536i

0+0.5000i

-0.3536+0.3536i

M ₆＝

0.5000

-0.3536+0.3536i

0-0.5000i

0.3536+0.3536i

M ₇＝

0.5000

-0.3536-0.3536i

0+0.5000i

0.3536-0.3536i

M ₈＝

0.5000

0.3536-0.3536i

0-0.5000i

-0.3536-0.3536i

5-3) in the situation that the quantity of the entity antenna of base station is four code books that use in carrying out the down link of multi-user MIMO communication system of non-unitary matrice precoding:

For example, in the situation that the quantity of the entity antenna of base station is four, can provide the included code word of code book of using in the down link of the multi-user MIMO communication system of carrying out non-unitary matrice precoding by following table 11:

Table 11

Send code book index	Transmission rank	1
			1	C 1，1＝W1(；，2)
2	C 2，1＝W1(；，3)
		3	C 3，1＝W1(；，4)
4	C 4，1＝W2(；，2)

5	C 5，1＝W2(；，3)
		6	C 6，1＝W2(；，4)
7	C 7，1＝W3(；，1)
		8	C 8，1＝W4(；，1)
9	C 9，1＝W5(；，1)
		10	C 10，1＝W5(；，2)
11	C 11，1＝W5(；，3)
		12	C 12，1＝W5(；，4)
13	C 13，1＝W6(；，1)
		14	C 14，1＝W6(；，2)
15	C 15，1＝W6(；，3)
		16	C 16，1＝W6(；，4)

The code word being included in above table 11 can be expressed as followsin:

C _1，1＝

0.5000

-0.5000

0.5000

-0.5000

C _2，1＝

-0.5000

-0.5000

0.5000

0.5000

C _3，1＝

-0.5000

0.5000

0.5000

-0.5000

C _4，1＝

0.5000

0-0.5000i

0.5000

0-0.5000i

C _5，1＝

-0.5000

0-0.5000i

0.5000

0+0.5000i

C _6，1＝

-0.5000

0+0.5000i

0.5000

0-0.5000i

C _7，1＝

0.5000

0.5000

0.5000

0.5000

C _8，1＝

0.5000

0+0.5000i

0.5000

0+0.5000i

C _9，1＝

0.5000

0.5000

0.5000

-0.5000

C _10，1＝

0.5000

0+0.5000i

-0.5000

0+0.5000i

C _11，1＝

0.5000

-0.5000

0.5000

0.5000

C _12，1＝

0.5000

0-0.5000i

-0.5000

0-0.5000i

C _13，1＝

0.5000

0.3536+0.3536i

0+0.5000i

-0.3536+0.3536i

C _14，1＝

0.5000

-0.3536+0.3536i

0-0.5000i

0.3536+0.3536i

C _15，1＝

0.5000

-0.3536，0.3536i

0+0.5000i

0.3536-0.3536i

C _16，1＝

0.5000

0.3536-0.3536i

0-0.5000i

-0.3536-0.3536i

6) in the situation that the quantity of the entity antenna of base station is four, the 4th example of the code book using in the down link of Single User MIMO communication system or multi-user MIMO communication system:

6-1) in the situation that the quantity of the entity antenna of base station is four code books that use in the down link of Single User MIMO communication system:

Here, spin matrix Urot and QPSK DFT matrix can be defined as foloows:

$U_{\mathrm{rot}}=\frac{1}{\sqrt{2}}\left[\begin{array}{cccc}1& 0& -1& 0\\ 0& 1& 0& -1\\ 1& 0& 1& 0\\ 0& 1& 0& 1\end{array}\right],$

$\mathrm{DFT}=0.5*\left[\begin{array}{cccc}1& 1& 1& 1\\ 1& j& -1& -j\\ 1& -1& 1& -1\\ 1& -j& -1& j\end{array}\right],$

Diag (a, b, c, d) is 4 * 4 matrixes, and the diagonal element of diag (a, b, c, d) is a, b, c, d, and all the other all elements are zero.

Code word W ₁, W ₂, W ₃, W ₄, W ₅and W ₆can be defined as follows:

${\mathrm{<figure-callout\; id="1"\; label="W"\; filenames="HPA00001280680200011.png"\; state="\{\{state\}\}">W</figure-callout>}}_1=\frac{1}{\sqrt{2}}*U_{\mathrm{rot}}*\left[\begin{array}{cccc}1& 1& 0& 0\\ 1& -1& 0& 0\\ 0& 0& 1& 1\\ 0& 0& 1& -1\end{array}\right]*\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& -1& 0\\ 0& 0& 0& -1\end{array}\right]=0.5*\left[\begin{array}{cccc}1& 1& 1& 1\\ 1& -1& 1& -1\\ 1& 1& -1& -1\\ 1& -1& -1& 1\end{array}\right]$

$W_2=\frac{1}{\sqrt{2}}*U_{\mathrm{rot}}*\left[\begin{array}{cccc}1& 1& 0& 0\\ j& -j& 0& 0\\ 0& 0& 1& 1\\ 0& 0& j& -j\end{array}\right]*\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& -1& 0\\ 0& 0& 0& -1\end{array}\right]=0.5*\left[\begin{array}{cccc}1& 1& 1& 1\\ j& -j& j& -\mathrm{<figure-callout\; id="1"\; label="j"\; filenames="HPA00001280680200011.png"\; state="\{\{state\}\}">j</figure-callout>}\\ 1& 1& -1& -1\\ j& -j& -j& j\end{array}\right]$

$W_3=\frac{1}{\sqrt{2}}*U_{\mathrm{rot}}*\left[\begin{array}{cccc}1& 1& 0& 0\\ 1& -1& 0& 0\\ 0& 0& 1& 1\\ 0& 0& j& -j\end{array}\right]*\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& -1& 0\\ 0& 0& 0& -1\end{array}\right]=0.5*\left[\begin{array}{cccc}1& 1& 1& 1\\ 1& -1& j& -\mathrm{<figure-callout\; id="1"\; label="j"\; filenames="HPA00001280680200011.png"\; state="\{\{state\}\}">j</figure-callout>}\\ 1& 1& -1& -1\\ 1& -1& -j& j\end{array}\right]$

$W_4=\frac{1}{\sqrt{2}}*U_{\mathrm{rot}}*\left[\begin{array}{cccc}1& 1& 0& 0\\ j& -j& 0& 0\\ 0& 0& 1& 1\\ 0& 0& 1& -1\end{array}\right]*\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& -1& 0\\ 0& 0& 0& -1\end{array}\right]=0.5*\left[\begin{array}{cccc}1& 1& 1& 1\\ j& -j& 1& -1\\ 1& 1& -1& -1\\ j& -j& -1& 1\end{array}\right]$

$W_5=\mathrm{diag}(\mathrm{1,1,1},-1)*\mathrm{DFT}=0.5*\left[\begin{array}{cccc}1& 1& 1& 1\\ 1& j& -1& -j\\ 1& -1& 1& -1\\ -1& j& 1& -j\end{array}\right]$

$W_6=\mathrm{diag}(1,\frac{(1+j)}{\sqrt{2}},j,\frac{(-1+j)}{\sqrt{2}})*\mathrm{DFT}=0.5*\left[\begin{array}{cccc}1& 1& 1& 1\\ \frac{(1+j)}{\sqrt{2}}& \frac{(-1+j)}{\sqrt{2}}& \frac{(-1-j)}{\sqrt{2}}& \frac{(1-j)}{\sqrt{2}}\\ j& -j& j& -j\\ \frac{(-1+j)}{\sqrt{2}}& \frac{(1+j)}{\sqrt{2}}& \frac{(1-j)}{\sqrt{2}}& \frac{(-1-j)}{\sqrt{2}}\end{array}\right]$

For example, in the situation that the quantity of the entity antenna of base station is four, according to the included matrix of the code book using in the down link of Single User MIMO communication system of the 4th example or code word, can be provided by following table 12:

Table 12

The code word being included in above table 12 can be expressed as followsin:

C _1，1＝

0.5000

-0.5000

0.5000

-0.5000

C _2，1＝

0.5000

0.5000

-0.5000

-0.5000

C _3，1＝

0.5000

-0.5000

-0.5000

0.5000

C _4，1＝

0.5000

0-0.5000i

0.5000

0-0.5000i

C _5，1＝

0.5000

0+0.5000i

-0.5000

0-0.5000i

C _6，1＝

0.5000

0-0.5000i

-0.5000

0+0.5000i

C _7，1＝

0.5000

0.5000

0.5000

0.5000

C _8，1＝

0.5000

0+0.5000i

0.5000

0+0.5000i

C _9，1＝

0.5000

0.5000

0.5000

-0.5000

C _10，1＝

0.5000

0+0.5000i

-0.5000

0+0.5000i

C _11，1＝

0.5000

-0.5000

0.5000

0.5000

C _12，1＝

0.5000

0-0.5000i

-0.5000

0-0.5000i

C _13，1＝

0.5000

0.3536+0.3536i

0+0.5000i

-0.3536+0.3536i

C _14，1＝

0.5000

-0.3536+0.3536i

0-0.5000i

0.3536+0.3536i

C _15，1＝

0.5000

-0.3536-0.3536i

0+0.5000i

0.3536-0.3536i

C _16，1＝

0.5000

0.3536-0.3536i

0-0.5000i

-0.3536-0.3536i

C _1，2＝

0.5000 0.5000

-0.5000 0.5000

0.5000 0.5000

-0.5000 0.5000

C _2，2＝

0.5000 0.5000

0.5000 0.5000

-0-5000 0.5000

-0.5000 0.5000

C _3，2＝

0.5000 0.5000

-0.5000 0.5000

-0.5000 0.5000

0.5000 0.5000

C _4，2＝

0.5000 0.5000

-0.5000 0.5000

0.5000 -0.5000

-0.5000 -0.5000

C _5，2＝

0.5000 0.5000

-0.5000 -0.5000

0.5000 -0.5000

-0.5000 0.5000

C _6，2＝

0.5000 0.5000

0.5000 -0.5000

-0.5000 -0.5000

-0.5000 0.5000

C _7，2＝

0.5000 0.5000

0+0.5000i 0+0.5000i

-0.5000 0.5000

0-0.5000i 0+0.5000i

C _8，2＝

0.5000 0.5000

0-0.5000i 0+0.5000i

-0.5000 0.5000

0+0.5000i 0+0.5000i

C _9，2＝

0.5000 0.5000

0-0.5000i 0+0.5000i

0.5000 -0.5000

0-0.5000i 0-0.5000i

C _10，2＝

0.5000 0.5000

0-0.5000i 0-0.5000i

0.5000 -0.5000

0-0.5000i 0+0.5000i

C _11，2＝

0.5000 0.5000

0+0.5000i 0.5000

-0.5000 0.5000

0-0.5000i 0.5000

C _12，2＝

0.5000 0.5000

0-0.5000i 0.5000

-0.5000 0.5000

0+0.5000i 0.5000

C _13，2＝

0.5000 0.5000

0.5000 0+0.5000i

-0.5000 0.5000

-0.5000 0+0.5000i

C _14，2＝

0.5000 0.5000

-0.50000 +0.5000i

-0.5000 0.5000

0.50000 +0.5000i

C _15，2＝

0.5000 0.5000

0.5000 -0.5000

0.5000 0.5000

-0.5000 0.5000

C _16，2＝

0.5000 0.5000

-0.3536+0.3536i 0.3536-0.3536i

0-0.5000i 0-0.5000i

0.3536+0.3536i -0.3536-0.3536i

C _1，3＝

0.5000 0.5000 0.5000

0.5000 -0.5000 0.5000

0.5000 0.5000 -0.5000

0.5000 -0.5000 -0.5000

C _2，3＝

0.5000 0.5000 0.5000

0.5000 -0.5000 -0.5000

0.5000 0.5000 -0.5000

0.5000 -0.5000 0.5000

C _3，3＝

0.5000 0.5000 0.5000

0.5000 0.5000 -0.5000

0.5000 -0.5000 -0.5000

0.5000 -0.5000 0.5000

C _4，3＝

0.5000 0.5000 0.5000

-0.5000 0.5000 -0.5000

0.5000 -0.5000 -0.5000

-0.5000 -0.5000 0.5000

C _5，3＝

0.5000 0.5000 0.5000

0+0.5000i 0-0.5000i 0+0.5000i

0.5000 0.5000 -0.5000

0+0.5000i 0-0.5000i 0-0.5000i

C _6，3＝

0.5000 0.5000 0.5000

0+0.5000i 0-0.5000i 0-0.5000i

0.5000 0.5000 -0.5000

0+0.5000i 0-0.5000i 0+0.5000i

C _7，3＝

0.5000 0.5000 0.5000

0+0.5000i 0+0.5000i 0-0.5000i

0.5000 -0.5000 -0.5000

0+0.5000i 0-0.5000i 0+0.5000i

C _8，3＝

0.5000 0.5000 0.5000

0-0.5000i 0+0.5000i 0-0.5000i

0.5000 -0.5000 -0.5000

0-0.5000i 0-0.5000i 0+0.5000i

C _9，3＝

0.5000 0.5000 0.5000

0.5000 -0.5000 0+0.5000i

0.5000 0.5000 -0.5000

0.5000 -0.5000 0-0.5000i

C _10，3＝

0.5000 0.5000 0.5000

0.5000 0+0.5000i 0-0.5000i

0.5000 -0.5000 -0.5000

0.50000 -0.5000i 0+0.5000i

C _11，3＝

0.5000 0.5000 0.5000

0+0.5000i 0-0.5000i 0.5000

0.5000 0.5000 -0.5000

0+0.5000i 0-0.5000i -0.5000

C _12，3＝

0.5000 0.5000 0.5000

0+0.5000i 0.5000 -0.5000

0.5000 -0.5000 -0.5000

0+0.5000i -0.5000 0.5000

C _13，3＝

0.5000 0.5000 0.5000

0.5000 0+0.5000i -0.5000

0.5000 -0.5000 0.5000

-0.5000 0+0.5000i 0.5000

C _14，3＝

0.5000 0.5000 0.5000

0.5000 -0.50000 -0.5000i

0.5000 0.5000 -0.5000

-0.5000 0.50000 -0.5000i

C _15，3＝

0.5000 0.5000 0.5000

0.3536+0.3536i -0.3536+0.3536i 0.3536-0.3536i

0+0.5000i 0-0.5000i 0-0.5000i

-0.3536+0.3536i 0.3536+0.3536i -0.3536-0.3536i

C _16，3＝

0.5000 0.5000 0.5000

-0.3536+0.3536i -0.3536-0.3536i 0.3536-0.3536i

0-0.5000i 0+0.5000i 0-0.5000i

0.3536+0.3536i 0.3536-0.3536i -0.3536-0.3536i

C _1，4＝

0.5000 0.5000 0.5000 0.5000

0.5000 -0.5000 0.5000 -0.5000

0.5000 0.5000 -0.5000 -0.5000

0.5000 -0.5000 -0.5000 0.5000

C _2，4＝

0.5000 0.5000 0.5000 0.5000

0+0.5000i 0-0.5000i 0+0.5000i 0-0.5000i

0.5000 0.5000 -0.5000 -0.5000

0+0.5000i 0-0.5000i 0-0.5000i 0+0.5000i

C _3，4＝

0.5000 0.5000 0.5000 0.5000

0.5000 -0.50000 +0.5000i 0-0.5000i

0.5000 0.5000 -0.5000 -0.5000

0.5000 -0.5000 0-0.5000i 0+0.5000i

C _4，4＝

0.5000 0.5000 0.5000 0.5000

0+0.5000i 0-0.5000i 0.5000 -0.5000

0.5000 0.5000 -0.5000 -0.5000

0+0.5000i 0-0.5000i-0.5000 0.5000

C _5，4＝

0.5000 0.5000 0.5000 0.5000

0.50000 +0.5000i -0.50000 -0.5000i

0.5000 -0.5000 0.5000 -0.5000

-0.5000 0+0.5000i 0.5000 0-0.5000i

C _6，4＝

0.5000 0.5000 0 .5000 0.5000

0.3536+0.3536i -0.3536+0.3536i -0.3536-0.3536i 0.3536-0.3536i

0+0.5000i 0-0.5000i 0+0.5000i 0-0.5000i

-0.3536+0.3536i 0.3536+0.3536i 0.3536-0.3536i -0.3536-0.3536i

6-2) in the situation that the quantity of the entity antenna of base station is four code books that use in the down link of multi-user MIMO communication system of carrying out unitary matrice precoding:

For example, can be by suitably combining two following matrix W ₃and W ₆subset carry out the code book using in the down link of multi-user MIMO communication system of design consideration the 4th example:

$W_3=\frac{1}{\sqrt{2}}*U_{\mathrm{rot}}*\left[\begin{array}{cccc}1& 1& 0& 0\\ 1& -1& 0& 0\\ 0& 0& 1& 1\\ 0& 0& j& -j\end{array}\right]*\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& -1& 0\\ 0& 0& 0& -1\end{array}\right]=0.5*\left[\begin{array}{cccc}1& 1& 1& 1\\ 1& -1& j& -\mathrm{<figure-callout\; id="1"\; label="j"\; filenames="HPA00001280680200011.png"\; state="\{\{state\}\}">j</figure-callout>}\\ 1& 1& -1& -1\\ 1& -1& -j& j\end{array}\right]$

$W_6=\mathrm{diag}(1,\frac{(1+j)}{\sqrt{2}},j,\frac{(-1+j)}{\sqrt{2}})*\mathrm{DFT}=0.5*\left[\begin{array}{cccc}1& 1& 1& 1\\ \frac{(1+j)}{\sqrt{2}}& \frac{(-1+j)}{\sqrt{2}}& \frac{(-1-j)}{\sqrt{2}}& \frac{(1-j)}{\sqrt{2}}\\ j& -j& j& -j\\ \frac{(-1+j)}{\sqrt{2}}& \frac{(1+j)}{\sqrt{2}}& \frac{(1-j)}{\sqrt{2}}& \frac{(-1-j)}{\sqrt{2}}\end{array}\right]$

For example, in the situation that the quantity of the entity antenna of base station is four, according to the included matrix of the code book using in the down link of the multi-user MIMO communication system of the 4th example or code word, can provide by following table 13:

Table 13

The code word being included in above table 13 can be represented as follows:

M ₁＝

0.5000

0.5000

0.5000

0.5000

M ₂＝

0.5000

-0.5000

0.5000

-0.5000

M ₃＝

0.5000

0+0.5000i

-0.5000

0-0.5000i

M ₄＝

0.5000

0-0.5000i

-0.5000

0+0.5000i

M ₅＝

0.5000

0.3536+0.3536i

0+0.5000i

-0.3536+0.3536i

M ₆＝

0.5000

-0.3536+0.3536i

0-0.5000i

0.3536+0.3536i

M ₇＝

0.5000

-0.3536-0.3536i

0+0.5000i

0.3536-0.3536i

M ₈＝

0.5000

0.3536-0.3536i

0-0.5000i

-0.3536-0.3536i

6-3) in the situation that the quantity of the entity antenna of base station is four code books that use in carrying out the down link of multi-user MIMO communication system of non-unitary matrice precoding:

For example, in the situation that the quantity of the entity antenna of base station is four, can provide the included code word of code book of using in the down link of the multi-user MIMO communication system of carrying out non-unitary matrice precoding by following table 14:

Table 14

Send code book index	Transmission rank	1
			1	C 1，1＝W1(；，2)
2	C 2，1＝W1(；，3)

3	C 3，1＝W1(；，4)
		4	C 4，1＝W2(；，2)
5	C 5，1＝W2(；，3)
		6	C 6，1＝W2(；，4)
7	C 7，1＝W3(；，1)
		8	C 8，1＝W4(；，1)
9	C 9，1＝W5(；，1)
		10	C 10，1＝W5(；，2)
11	C 11，1＝W5(；，3)
		12	C 12，1＝W5(；，4)
13	C 13，1＝W6(；，1)
		14	C 14，1＝W6(；，2)
15	C 15，1＝W6(；，3)
		16	C 16，1＝W6(；，4)

The code word being included in above table 14 can be expressed as followsin:

C _1，1＝

0.5000

-0.5000

0.5000

-0.5000

C _2，1＝

0.5000

0.5000

-0.5000

-0.5000

C _3，1＝

0.5000

-0.5000

-0.5000

0.5000

C _4，1＝

0.5000

0-0.5000i

0.5000

0-0.5000i

C _5,1＝

0.5000

0+0.5000i

-0.5000

0-0.5000i

C _6，1＝

0.5000

0-0.5000i

-0.5000

0+0.5000i

C _7，1＝

0.5000

0.5000

0.5000

0.5000

C _8，1＝

0.5000

0+0.5000i

0.5000

0+0.5000i

C _9，1＝

0.5000

0.5000

0.5000

-0.5000

C _10.1＝

0.5000

0+0.5000i

-0.5000

0+0.5000i

C _11，1＝

0.5000

-0.5000

0.5000

0.5000

C _12，1＝

0.5000

0-0.5000i

-0.5000

0-0.5000i

C _13，1＝

0.5000

0.3536+0.3536i

0+0.5000i

-0.3536+0.3536i

C _14，1＝

0.5000

-0.3536+0.3536i

0-0.5000i

0.3536+0.3536i

C _15，1＝

0.5000

-0.3536-0.3536i

0+0.5000i

0.3536-0.3536i

C _16，1＝

0.5000

0.3536-0.3536i

0-0.5000i

-0.3536-0.3536i

Various examples according to the code word of the quantity of the transmission rank in the down link of Single User MIMO communication system and multi-user MIMO communication system and antenna have below been described.Can use various types of schemes and shape to revise above-mentioned code word, code word is not limited to above-mentioned example.For example, the open and instruction based on providing at this, those skilled in the art can obtain identical in fact code word by changing the phase place (for example,, by complex exponential is multiplied each other with the row of code word) of the row of above-mentioned code word.As another example, those skilled in the art can be multiplied each other " 1 " and the row of code word.

Yet the performance of code book or attribute may not can change by changing the phase place of the row of code word.Therefore, should be understood that by changing code book that the phase place of the row of code word produces and comprising that to change the code book of phase place original code word before identical or equivalent.In addition, it should be understood that the code book that the row of the original code word by exchange code book produce is identical or equivalent with the code book that comprises exchange original code word before.For the sake of simplicity, by omit to by change in the code book that the phase place of the row of original code word produces or code book that row by exchange original code word produce in the explanation of included particular value.

In the situation that the quantity of the antenna of base station is four, described code book hypothesis MIMO communication system is used 4 bit code books conventionally.Yet embodiment is not limited to this.For example, in the situation that comprise and the above-mentioned 6 bit code books that are included in the code word that code word is identical or essence is identical in 4 bit code books, should understand 6 bit code books and can be equivalent to above-mentioned exemplary code book.

7) in the situation that the quantity of the entity antenna of base station is eight, the code book using in the down link of Single User MIMO communication system:

For example, in the situation that the quantity of the entity antenna of base station is eight, the code book using in the down link of Single User MIMO communication system can be designed to be provided by following equation 9:

$W_0=\frac{1}{\sqrt{8}}\left[\begin{array}{cccccccc}1& 1& 1& 1& 1& 1& 1& 1\\ 1& e^{\mathrm{j\&pi;}/4}& e^{\mathrm{j\&pi;}/2}& e^{j3\mathrm{\&pi;}/4}& e^{\mathrm{j\&pi;}}& e^{j5\mathrm{\&pi;}/4}& e^{j3\mathrm{\&pi;}/2}& e^{j7\mathrm{\&pi;}/4}\\ 1& e^{\mathrm{j\&pi;}/2}& e^{\mathrm{j\&pi;}}& e^{j3\mathrm{\&pi;}/2}& 1& e^{\mathrm{j\&pi;}/2}& e^{\mathrm{j\&pi;}}& e^{j3\mathrm{\&pi;}/2}\\ 1& e^{j3\mathrm{\&pi;}/4}& e^{j3\mathrm{\&pi;}/2}& e^{\mathrm{j\&pi;}/4}& e^{\mathrm{j\&pi;}}& e^{j7\mathrm{\&pi;}/4}& e^{\mathrm{j\&pi;}/2}& e^{j5\mathrm{\&pi;}/4}\\ 1& e^{\mathrm{j\&pi;}}& 1& e^{\mathrm{j\&pi;}}& 1& e^{\mathrm{j\&pi;}}& 1& e^{\mathrm{j\&pi;}}\\ 1& e^{j5\mathrm{\&pi;}/4}& e^{\mathrm{j\&pi;}/2}& e^{j7\mathrm{\&pi;}/4}& e^{\mathrm{j\&pi;}}& e^{\mathrm{j\&pi;}/4}& e^{j3\mathrm{\&pi;}/2}& e^{j3\mathrm{\&pi;}/4}\\ 1& e^{j6\mathrm{\&pi;}/4}& e^{j\mathrm{\&pi;}}& e^{\mathrm{j\&pi;}/2}& 1& e^{j3\mathrm{\&pi;}/2}& e^{\mathrm{j\&pi;}}& e^{j\mathrm{\&pi;}/2}\\ 1& e^{j7\mathrm{\&pi;}4}& e^{j3\mathrm{\&pi;}/2}& e^{j5\mathrm{\&pi;}/4}& e^{\mathrm{j\&pi;}}& e^{j3\mathrm{\&pi;}/4}& e^{\mathrm{j\&pi;}/2}& e^{\mathrm{j\&pi;}/4}\end{array}\right]---\left(9\right).$

The matrix being included in for the code book of Single User MIMO communication system can be confirmed as being provided by following table 15:

Table 15

With reference to above table 15, in the situation that transmission rank is 4, can be based on W ₀(; , 123 4), W ₀(; , 34 56), W ₀(; , 567 8), W ₀(; , 781 2), W ₀(; , 135 7), W ₀(; , 246 8), W ₀(; , 571 4) and W ₀(; , 682 3) in any one produce pre-coding matrix.Here, W _k(; , n m o p) and represent to comprise W _kthe matrix of n column vector, m column vector, o column vector and p column vector.

In the situation that transmission rank is 3, can be based on W ₀(; , 12 3), W ₀(; , 34 5), W ₀(; , 56 7), W ₀(; , 7 81), W ₀(; , 13 5), W ₀(; , 24 6), W ₀(; , 57 1) and W ₀(; , 68 2) in any one produce pre-coding matrix.Here, W _k(; , n m o) and represent to comprise W _kthe matrix of n column vector, m column vector and o column vector.

In the situation that transmission rank is 2, can be based on W ₀(; , 1 2), W ₀(; , 3 4), W ₀(; , 5 6), W ₀(; , 7 8), W ₀(; , 1 3), W ₀(; , 2 4), W ₀(; , 5 7) and W ₀(; , 6 8) in any one produce pre-coding matrix.Here, W _k(; , n m) and represent to comprise W _kn column vector and the matrix of m column vector.

In the situation that transmission rank is 1, can be based on W ₀(; , 1), W ₀(; , 2), W ₀(; , 3), W ₀(; , 4), W ₀(; , 5), W ₀(; , 6), W ₀(; , 7) and W ₀(; , 8) in any one produce pre-coding matrix.Here, W _k(; , n) represent W _kthe matrix of n column vector.

the code book upgrading

According to the MIMO communication system of exemplary embodiment, can upgrade code book according to the time correlation coefficient () that is formed at the channel between at least one user and base station.

In the environment changing according to the time at channel, be unsuitable for using fixing code book.Thereby MIMO communication system can detect the change of channel upgrades code book adaptively.

Conventionally, can be provided by following equation 10 modeling of channel:

H _τ＝ρ·H _τ-1+Δ (10)

Wherein, H _τbe illustrated in channel vector or the channel matrix of τ in the time interval, ρ represents to be greater than O and is less than 1 time correlation coefficient, and Δ represents recombination noise, and the average with Δ is zero and the normal distribution that is changed to 1-ρ of Δ.

According in the MIMO communication system of exemplary embodiment, terminal can be according to above equation coefficient correlation 10 computing time (ρ).Terminal can feed back to base station by the time coefficient (ρ) of calculating.Code book can be upgraded by the time correlation coefficient (ρ) based on feedback adaptively in base station.

Here, suppose that the code book before code book upgrades is

the code book upgrading is

the i element that represents the code book of renewal, B represents the quantity of feedback bits.

The pre-coding matrix using in the time interval in τ-1 is F _τ-1situation under, according to base station on the one hand, can use

calculate new pre-coding matrix F _τ. it is the element of the code book of renewal.With F _τthe corresponding F of initial value ₀it can be the above-mentioned pre-coding matrix for two, four and eight transmitting antennas.Especially, can use previous pre-coding matrix F _τ-1element with the code book upgrading

represent F _τ, as following equation 11 provides:

$F_{\mathrm{\&tau;}}={\widetilde{\mathrm{\&Theta;}}}_i{F}_{\mathrm{\&tau;}-1}---\left(11\right).$

In multi-user MIMO communication system, F _τit can be the pre-coding matrix for alone family.Therefore, each user's F _τcan be different.Base station can send by poll active terminal and combination and the corresponding F of each user of data _τproduce pre-coding matrix.

$\begin{array}{cc}1)& \left\{\mathrm{\&theta;}\right\}=\{{\mathrm{\&Theta;}}_1,...,{\mathrm{\&Theta;}}_{2^B}\}\end{array}$ Design

For example, element or code word there is N _t* N _tdimension.Each element can be unitary matrice.

can equi-spaced apart.

design can change, two exemplary arrangement will be described here.

(1) can propose to comprise according to following equation 12 the full unitary matrice of full unitary matrice

${\mathrm{\&Theta;}}_l={\mathrm{\&Phi;}}^{l}D,l=1,...2^B$

φ _i∈{1，2，…，2 ^B} (12)

Wherein, D represents to have N _t* N _tthe DFT matrix of dimension.

For example, work as N _t=4 o'clock, for [the φ of number of bits of feedback B ₁, φ ₂, φ ₃, φ ₄] can be confirmed as providing by following table 16:

Table 16

B	[φ 1，φ 2，φ 3，φ 4]
		B＝2	[1，2，3，4]
B＝3	[2，4，5，6]
		B＝4	[1，3，4，8]
B＝5	[11，18，22，23]

For example, wherein, B=3, N _t=2,

Can provide by following table 17

Table 17

(2) diagonal unitary

Can propose to comprise diagonal unitary according to following equation 13

Equation 13

Θ _l＝Φ ^l，l＝1，...，2 ^B

$\mathrm{\&Phi;}=\mathrm{diag}\left[\begin{array}{cccc}{e}^{j2\mathrm{\&pi;}{\mathrm{\&phi;}}_1/2^B}& e^{j2\mathrm{\&pi;}{\mathrm{\&phi;}}_2/2^B}& ...& e^{j2\mathrm{\&pi;}{\mathrm{\&phi;}}_{N^t}/2^B}\end{array}\right]$

φ _i∈{1，2，…，2 ^B} (13)。

With reference to above-mentioned equation 13, can use diagonal matrix design

for example, work as N _t=4, for [the φ of the quantity B of feedback bits ₁, φ ₂, φ ₃, φ ₄] can be confirmed as providing by following table 18:

Table 18

B	[φ 1，φ 2，φ 3，φ 4]
		B＝2	[1，2，3，4]
B＝3	[2，4，5，6]
		B＝4	[1，3，4，8]
B＝5	[11，18，22，23]

$\begin{array}{cc}2)& \left\{\widetilde{\mathrm{\&theta;}}\right\}=\{{\widetilde{\mathrm{\&Theta;}}}_1,...,{\widetilde{\mathrm{\&Theta;}}}_{2^B}\}\end{array}$ Calculating:

According in the MIMO communication system of exemplary embodiment, base station or user terminal can be according to the time correlation coefficient updates of channel

thereby produce new code book

For i=1,2,3 ..., 2 ^b, can calculate

in this example, can use various types of schemes that the code book of renewal is provided.Below, two exemplary arrangement will be described.Here, I representation unit matrix.

(1) first scheme

In the first scheme, can calculate according to the code book of the renewal of exemplary embodiment with following equation 14

Equation 14

${\widetilde{\mathrm{\&Theta;}}}_i=\underset{{\widetilde{\mathrm{\&Theta;}}}_i}{\arg \min }{\left|\right|{\mathrm{\&Psi;}}_i(\mathrm{\&rho;},{\mathrm{\&Theta;}}_i)-{\widetilde{\mathrm{\&Theta;}}}_i\left|\right|}_F---\left(14\right).$

In above equation 14, || x|| _fthe Frobenious norm that represents x.

Here, suppose right

carry out singular value decomposition (SVD),

in this example, can use the solution of equatioies 14 more than equation 15 calculating below:

${\widetilde{\mathrm{\&Theta;}}}_i={\mathrm{\&Phi;}}_i{B}_i^{*}---\left(15\right).$

In the first scheme, can calculate the code book upgrading according to above equation 14 or above equation 15

(2) schemes

In alternative plan, can use following equation 16 to calculate the code book upgrading

${\widetilde{\mathrm{\&Theta;}}}_i={\left[{\mathrm{\&Psi;}}_i{(\mathrm{\&rho;},{\mathrm{\&Theta;}}_i)}^{*}{\mathrm{\&Psi;}}_i(\mathrm{\&rho;},{\mathrm{\&Theta;}}_i)\right]}^{-1/2}{\mathrm{\&Psi;}}_i(\mathrm{\&rho;},{\mathrm{\&Theta;}}_i)---\left(16\right).$

Can dynamically calculate according to the code book of the renewal of the first scheme or alternative plan calculating based on time correlation coefficient

Can be by time correlation coefficient quantization.Can be stored in memory with the corresponding code book upgrading of quantized value.In this example, the code book of renewal needn't be by dynamic calculation.Especially, in the situation that terminal feeds back to base station by time correlation coefficient, any one code book can be selected in base station from be stored in the code book of a plurality of renewals memory.

the code book upgrading various examples

The code book that can upgrade according to various calculation of parameter as mentioned above,

below, description is depended on feedback bits quantity, or design

example.

1) work as N _t=4, the quantity B=4 of feedback bits,

comprise full unitary matrice, the first scheme (that is, using above-mentioned equation 14 or above-mentioned equation 15), according to the code book of time correlation coefficient update

example can be as follows:

(1) time correlation coefficient=0

(2) time correlation coefficient=0.7

(3) time correlation coefficient=0.75

(4) time correlation coefficient=0.8

(5) time correlation coefficient=0.85

(6) time correlation coefficient=0.9

(7) time correlation coefficient=0.95

2) at the quantity B=4 of feedback bits, comprise diagonal unitary, used in the situation of alternative plan (that is, described equation 16), according to the code book of time correlation coefficient update

example can be as follows:

(1) time correlation coefficient=0

(2) time correlation coefficient=0.7

(3) time correlation coefficient=0.75

(4) time correlation coefficient=0.8

(5) time correlation coefficient=0.85

(6) time correlation coefficient=0.9

(7) time correlation coefficient=0.95

3) at N _t=2, the quantity B=3 of feedback bits,

comprise full unitary matrice, in the situation of the first scheme (above equation 14 or equation 15) of having used, according to the code book of time correlation coefficient update

example can be as follows:

(1) time correlation coefficient=0

(2) time correlation coefficient=0.7

(3) time correlation coefficient=0.75

(4) time correlation coefficient=0.8

(5) time correlation coefficient=0.85

(6) time correlation coefficient=0.9

(7) time correlation coefficient=0.95

Except above example, can be according to the quantity of the transmitting antenna of the quantity of various time coefficients, feedback bits, base station or

differently calculate here, further describe omission is relative for the sake of simplicity.

Fig. 3 is the flow chart illustrating according to the MIMO communication means of exemplary embodiment.Should be understood that one or more operations that above-mentioned one or more equipment (for example, base station) can execution graph 3.

With reference to Fig. 3, at operation S310, the code book of design for example can be stored in memory in advance.The exemplary design scheme of code book described above.Identical code book can be stored and use to base station or user terminal.

At operation S320, can identify the state that is formed at the channel between base station and user terminal.

For example, base station can send to user terminal by known pilot signal, and user terminal can be used this pilot signal to estimate to be formed at the channel between base station and user terminal.The channel status of the channel of estimating can be represented as channel information.Channel information can comprise channel condition information, channel quality information or channel directional information.Channel information can be fed back to base station from user terminal.Base station can based on feedback channel information identification channel state.

At operation S330, can determine adaptively transmission rank.For example, can determine adaptively transmission rank according to the data of the channel status of attainable total data transfer rate, user/user terminal or the expectation of user/user terminal.

At operation S340, can determine pre-coding matrix by consideration channel information and the transmission rank based on being included in a plurality of matrixes in code book.For example, can be based on channel information selection matrix from a plurality of matrixes.Thereby the large I of the matrix of selecting is used as pre-coding matrix according to transmission rank.

At operation S350, use definite pre-coding matrix to carry out precoding to data stream.

Fig. 4 is the flow chart illustrating according to the MIMO communication means of another embodiment.Should be understood that one or more operations that above-mentioned one or more equipment (for example, base station) can execution graph 4.

With reference to Fig. 4, at operation S410, the code book of design for example can be stored in memory in advance.

At operation S420, can identify the channel status that is formed at the channel between user and base station.For example, base station can be based on carrying out identification channel state from the channel information of user terminal feedback.

At operation S430, time correlation coefficient that can identification channel.The time correlation coefficient that user terminal can calculate the time correlation coefficient of channel and quantize to calculate.User terminal can feed back to base station by quantized value.

At operation S440, can upgrade code book according to the time correlation coefficient (ρ) that is formed at the channel between at least one user and base station.Described the scheme of upgrading code book in the above, therefore further described omission is relative.

At operation S450, can use the code book of renewal to produce pre-coding matrix.For example, at the code book upgrading, be

the pre-coding matrix previously having used is F _τ-1situation under, can use

produce the pre-coding matrix of current use.

At operation S460, with the pre-coding matrix producing, data stream is carried out to precoding.

According to above-mentioned specific embodiment, can be with improving data transmission rate according to the code book of the quantity optimization of channel circumstance, transmission rank and/or feedback bits.

The above-mentioned method that comprises MIMO communication means can be recorded, stores or be fixed on and comprise in one or more computer-readable mediums of the program command by computer-implemented, so that processor is carried out or execution of program instructions.Medium also can comprise independent program command, data file, data structure etc. or their combination.Medium and program command can be special design and structure, or they can be known and available for the technical staff of computer software fields.The example of computer-readable medium comprises that magnetizing mediums (for example, hard disk, floppy disk and tape), light medium (for example, CD ROM dish and DVD), magnet-optical medium (for example, CD) and special configuration for storing the hardware unit with execution of program instructions, for example, read-only memory (ROM), random access memory (RAM), flash memory etc.The example of program command comprises machine code and file, and machine code is for example produced by compiler, the more high-level code that file including can be used interpreter to carry out by computer.Above-mentioned hardware unit can be configured as one or more software modules, to carry out above-mentioned operation and method, vice versa.In addition, computer-readable storage or recording medium can be distributed in the computer system of networking, can store and object computer instructions or code in the mode of disperseing.

Computer or computer system can comprise the microprocessor for example, being electrically connected to bus, user interface, modulator-demodulator (, baseband chipsets), Memory Controller and flash memory device.Flash memory device can be stored N Bit data by Memory Controller.Described N bit by or will be by microprocessor processes, N can be 1 or be greater than 1 integer.In the situation that computer or computing system are mobile device, also can provide in addition battery to think that computer or computing system provide operating voltage.For those of ordinary skill in the art, it is apparent that, computer or computing system also can comprise application chip group, camera image processor (CIS), mobile dynamic random access memory (DRAM) etc.Memory Controller and flash memory device can form the solid-state drive/dish (SSD) that uses nonvolatile memory storage data.

A plurality of exemplary embodiments have below been described.However, it should be understood that and can carry out various modifications.For example, if carry out above-mentioned technology and/or combine in a different manner the element in above-mentioned system, framework, device or circuit and/or replace described element with other element or equivalent with different orders, can realize suitable result.Therefore, within other execution modes fall into the scope of claim.

Claims (16)

1. a base station for alone family multiple-input and multiple-output MIMO communication system, comprising:

Memory, a plurality of code word matrix C that storage comprises _1,2, C _2,2, C _3,2, C _4,2, C _5,2, C _6,2, C _7,2, C _8,2, C _9,2, C _10,2, C _11,2, C _12,2, C _13,2, C _14,2, C _15,2and C _16,2code book;

Precoder, is used described code book to the data flow being sent out is carried out to precoding,

Wherein, by a plurality of code word matrix described in lower table definition:

2. base station as claimed in claim 1, wherein, precoder at least one code word matrix based in described a plurality of code word matrix is calculated pre-coding matrix, and uses pre-coding matrix to carry out precoding to data stream.

3. base station as claimed in claim 1, also comprises:

Message recipient, from terminal receiving feedback information,

Wherein, precoder is used feedback information and code book to carry out precoding to data stream.

4. base station as claimed in claim 3, wherein, precoder is based on calculating pre-coding matrix with the corresponding code word matrix of feedback information in described a plurality of code word matrix, and uses pre-coding matrix to carry out precoding to data stream.

5. base station as claimed in claim 3, wherein, feedback information comprises the index information of terminal preferred code word matrix from described a plurality of code word matrix.

6. base station as claimed in claim 1, also comprises four transmitting antennas, and wherein, described code book is for transmission rank 2.

7. a base station for multi-user MIMO communication system, described base station comprises:

Memory, a plurality of code word matrix C that storage comprises _1,2, C _2,2, C _3,2, C _4,2, C _5,2, C _6,2, C _7,2, C _8,2, C _9,2, C _10,2, C _11,2, C _12,2, C _13,2, C _14,2, C _15,2and C _16,2code book;

Precoder, is used described code book to the data flow being sent out is carried out to precoding,

Wherein, by a plurality of code word matrix described in lower table definition:

8. base station as claimed in claim 7, also comprises:

Message recipient, from least two terminal receiving feedback informations,

Wherein, at least one feedback information that precoder use receives from described at least two terminals and described code book carry out precoding at least one data flow.

9. a terminal for MIMO communication system, described terminal comprises:

Memory, a plurality of code word matrix C that storage comprises _1,2, C _2,2, C _3,2, C _4,2, C _5,2, C _6,2, C _7,2, C _8,2, C _9,2, C _10,2, C _11,2, C _12,2, C _13,2, C _14,2, C _15,2and C _16,2code book;

Feedback unit, the feedback information that the preferred code word matrix with described a plurality of code word matrix is associated feeds back to base station,

Wherein, by a plurality of code word matrix described in lower table definition:

10. terminal as claimed in claim 9, also comprises:

Channel estimating unit, estimates the channel between base station and terminal,

Wherein, feedback unit feeds back to base station by the definite feedback information of channel based on estimating.

11. 1 kinds of method for precoding for the base station of Single User MIMO communication system, described method comprises:

Reference to storage, described memory stores a plurality of code word matrix C that comprise _1,2, C _2,2, C _3,2, C _4,2, C _5,2, C _6,2, C _7,2, C _8,2, C _9,2, C _10,2, C _11,2, C _12,2, C _13,2, C _14,2, C _15,2and C _16,2code book;

Use described code book to the data flow being sent out is carried out to precoding,

Wherein, by a plurality of code word matrix described in lower table definition:

12. methods as claimed in claim 11, wherein, described precoding step comprises:

At least one code word matrix based in described a plurality of code word matrix is calculated pre-coding matrix;

Use pre-coding matrix to carry out precoding to data stream.

13. methods as claimed in claim 11, also comprise:

From terminal receiving feedback information,

Wherein, described precoding step comprises: with feedback information and described code book, data stream is carried out to precoding.

14. 1 kinds of method for precoding for the base station of multi-user MIMO communication system, described method comprises:

Reference to storage, described memory stores a plurality of code word matrix C that comprise _1,2, C _2,2, C _3,2, C _4,2, C _5,2, C _6,2, C _7,2, C _8,2, C _9,2, C _10,2, C _11,2, C _12,2, C _13,2, C _14,2, C _15,2and C _16,2code book;

Use described code book to the data flow being sent out is carried out to precoding,

Wherein, by a plurality of code word matrix described in lower table definition:

15. 1 kinds of methods of operation for the terminal of MIMO communication system, described method comprises:

Reference to storage, described memory stores a plurality of code word matrix C that comprise _1,2, C _2,2, C _3,2, C _4,2, C _5,2, C _6,2, C _7,2, C _8,2, C _9,2, C _10,2, C _11,2, C _12,2, C _13,2, C _14,2, C _15,2and C _16,2code book;

The feedback information that preferred code word matrix with described a plurality of code word matrix is associated feeds back to base station,

Wherein, by a plurality of code word matrix described in lower table definition:

16. methods as claimed in claim 15, also comprise:

Estimate the channel between base station and terminal;

Channel based on estimating produces feedback information.

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